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Electric Circuits

Page history last edited by Aneesha Asthana 3 years, 10 months ago

Electric Circuits Practice Problems

 

Introduction to Electric Circuits

 

 

Operational Definition to get a Bulb to Light

 

Procedure: 

 

1. Use the wire(s) to make a closed loop.

2. Make sure that the loop involves both the positive and negative sides of the battery.

3. The loop must also include the metal screw on the lower half of the bulb, and the metal nub at the very bottom of the light bulb.

 
 

 

 

Electric Circuit Cornerstones

Just like in our Electric Charge Unit, we created a handful of simple rules for circuits based on what we observed during the lab. We will then apply these rules to understand increasingly complex circuits. 

 

1.  The amount of current in a series circuit is the same throughout the series. 

   

2. The relationship between current through the battery and total resistance of the circuit is inversely proportional. If the total resistance increases, then the current through the battery decreases, and vice versa.

 

3. Adding a bulb (or network of bulbs) in series increases the total resistance of the circuit.

 

4. Adding a bulb (or network of bulbs) in parallel decreases the total resistance of the circuit.

 

5. The distribution of current at a junction depends on the relative resistance of the pathways. More of the current takes the path with less resistance. 

 

6. Bulbs (or networks of bulbs) are independent when they are in parallel with each other and directly connected to the battery. Directly connected to the battery means that the network of items in parallel must not be in series with anything else except the battery. 

 

7. Any bulbs (or network of bulbs) in series are always dependent of each other. 

 
 

 

Evidence for Electric Circuit Cornerstones

 

1. One way to think about why the same amount of current flows through bulbs connected in series is because they are on the same pathway. Experimentally, we saw in the nickel chrome wire demo that when electricity is run through the wire (in series), the temperature is even throughout the wire. This implies that the current is the same everywhere in the wire since the cause of the rise in temperature is the electric current. Another piece of evidence supporting this cornerstone is what happens when you wire two bulbs in series. If the current through the two bulbs weren't equal, one of the bulbs would be visibly brighter than the other ones - but this doesn't happen! Therefore, current though elements in series is the same.    
2. If the total resistance of the circuit increases, then the current through the battery decreases. If the total resistance of the circuit decreases, then the current through the battery increases. We saw that when a second bulb was added in series to the first both bulbs got dimmer (top example). This implies the current through each bulb dropped. It's intuitive to expect that adding another poor conductor in a row with the first will increase the overall resistance. 

 

Another thing we observed in the lab is what happens if you add a new bulb directly in parallel with only one of two bulbs which started in series (as the example at the bottom shows). In this case A and B begin in series but bulb C is added in parallel with only bulb B. When we did this, we noticed that bulb A became brighter. It makes sense that the new circuit would have less overall resistance because a new pathway was added. We know the current through the battery increased because the current through bulb A went up (i.e. it got brighter) and the battery and bulb A are in series (see cornerstone #1). 

 

 

 

3. Adding a bulb (or network of bulbs) in series increases the total resistance of the circuit. We can see this when we add a second bulb in series to the first bulb. The single bulb circuit will be brighter than either of the two bulbs in series. This implies there is more current going through the single bulb, and by the previous cornerstone we know that the relationship between overall current and overall resistance is inverse.    

4. Adding a bulb (or a network of bulbs) in parallel decreases the resistance of the circuit. As a result, the current through battery increases when a new bulb is added in parallel (as shown to the right). We deduce this by seeing that all three bulbs are about the same brightness and since brightness is dependent on current, there has to be twice the amount of current in the 2nd battery (since there are now two equally bright bulbs on separate pathways). 

 

A good way to think about this is: creating a parallel circuit adds another pathway in the circuit, decreasing total resistance, which in turn increases the current through the battery. Adding more bulbs is analogous to adding more straws to blow into; it's now easier for the air to flow (i.e. better conductor). 

 

If you are still confused about why resistance in parallel decreases, here are some additional ways to understand why: think of circuits like the toll booths on a highway. Imagine if there's only one (This would represent the series circuit); all the cars (in a circuit, this is equivalent to the current) would have to go through that one toll booth. If you think of the highway as a circuit path, and the toll booth as a resistor, you'll notice that the flow of the current/cars decreases because the one booth is the only place the cars can go through. However, if someone added more toll booths in parallel, although this would technically mean more resistors, this also increases the current because the cars/current have more pathways to follow (Since they have more booths they can go to).

 

Finally another way to think about it: in a series circuit, everything follows one path. In that path, there can be one or more resistors which means there's less current flowing. However, in parallel, the current splits up, and is able to follow more than one path. This means the current increases. 

 

 

 
 

5. The distribution of current at a junction depends on the relative resistance of the pathways. More of the current takes the path of less resistance, and thus more current will flow down the circuit with less resistance. For the circuits to the right, let's assume that the current through the batteries in both circuits is 4A. In the first circuit, the current is divided into 2A for each parallel pathway because the resistors are identical (each path has only one light bulb). However, in the second circuit, the first pathway has 3A through it because it has less resistance than the second one, as the bulbs in series increase resistance (see cornerstones #2 & 3).

 

Another way this cornerstone can be supported would be to hook up an ammeter to the circuit and measure the currents in different parallel pathways. 

 

 

6. Bulbs (or networks of bulbs) are independent when they are parallel with each other but not in series with anything else. In other words, independent pathways have their own direct connection to the battery (since they are only connected in parallel with other bulbs or networks of bulbs). We know that this is true because when we built the circuit at the right unscrewing A had no effect on the brightness of either B or C. Alternatively if we modified B or C it didn't affect A. 

 

Tip: B and C are in series with each other (i.e. not directly connected to the battery) so they are dependent of each other. If you unscrew B, C will go out and visa versa. 

 
 
7. Bulbs which are parallel to each other, but in series with any other circuit element are dependent of each other. For example, in the circuit at the right, bulbs B and C are dependent of each other even though they are parallel to each other. We saw that if you unscrew C, B changes its brightness.   

 

A Way to Visualize Electric Circuits

 

The circuit at the right shows a constant current flowing through a single bulb. The current's size can be determined by the brightness of the light bulb. 

 

 

 

Ammeters and Voltmeters

 

Ammeter

The ammeter is a tool which measures the amount of current flowing through it. Ideally, a ammeter would have a resistance of zero in order to have little effect on the circuit, as it is wired in series.

The ammeter has 3 inputs (red sockets) and one ground (black socket). The black probe plugs into the input labeled 0, and the red probe plugs into one of the 3 red sockets. the settings of the ammeter are 5A, 0.5A and 0.05A. 

This number represents the maximum reading of the scale. For example, if we had a 0.5A current flowing through the meter, and the probe was plugged into the 0.5 socket, the needle would reach the 6th bold tick mark,

while a 0.5A current in a 5A socket would only reach half way to the second tick mark.

 

If the needle doesn't reach the first tick mark when measuring, we know we need to increase the fineness of the scale. If it reaches the far right of the scale, we know we need to reduce the fineness of the scale.

This means that whenever we reduce the maximum reading of the scale, our reading has more sig figs, as the tick marks on the scale have lower values, while increasing the maximum reading reduces the number of sig-figs we have.

 

When measuring the current through a path in the circuit with ammeter, we hook it up in series. We do this, because every component in a series circuit has the same amount of current flowing through it.

 

In this example, The ammeter measures the current through the resistor, as all components in series receive the same amount of current.

 

Tips:

  • When using an ammeter, is the needle appears to move to the left, it might be wired into the circuit backwards, or the probes may have been switched.
  • make sure that the switch left of the black socket is set to the two parallel lines, as in freshmen physics we only look at DC electricity.   

 

Voltmeter

 

The voltmeter is a tool which measure the voltage across a component or components of a circuit. Ideally, a voltmeter would have a extremely high resistance in order to not effect the circuit, as it is wired in parallel. 

Like the ammeter, the voltmeter has 3 inputs (red sockets) and one ground (black socket). The black probe plugs into the input labeled 0, and the red probe plugs into one of the 3 red sockets. The settings of the voltmeter are 30V, 15V and 3V. 

This number represents the maximum reading of the scale. For example, if we had a voltage of 3V across a component, and the probe was plugged into the 3V socket, the needle would reach the fourth bold tick mark,

while a 3V voltage in a 15V socket would only reach three-fifths of the way to the second tick mark.

 

Once again like the Ammeter, If the needle doesn't reach the first tick mark when measuring, we know we need to increase the fineness of the scale. If it reaches the far right of the scale, we know we need to reduce the fineness of the scale.

This means that whenever we reduce the maximum reading of the scale, our reading has more sig figs, as the tick marks on the scale have lower values, while increasing the maximum reading reduces the number of sig-figs we have.

 

When measuring the current through a path in the circuit with voltmeter, we hook it up in parallel. We do this, because every loop in a parallel circuit has the same total voltage, and by adding a voltmeter in parallel, it create a new loop.

In this example, The voltmeter is measuring not only the voltage across the battery, but the voltage across the resistor, as all three of these components are in a parallel network and would therefore have the same voltage across them.

 

Tips:

  • When using an voltmeter, is the needle appears to move to the left, it might be wired into the circuit backwards, or the probes may have been switched.
  • make sure that the switch left of the black socket is set to the two parallel lines, as in freshmen physics we only look at DC electricity.   

 

 

Current & Resistance Lab

 

In the current and resistance lab we found that if you double the resistance the current gets cut in half (and visa versa). We used this pattern to build algebraic rules for how resistance works for identical resistors. R stands for the resistance of the identical resistors and n for the number of resistors wired in either series or parallel. 

 

 

 

 

 

Example 1: 

Find the total resistance of two identical 45 ohm resistors wired in series.  

 

Explanation

The circuit is in a series so all you have to do is follow a simple equation to find out the total resistance of the circuit: 

 

 

Following this, you should have gotten 90 Ω. All you had to do was multiply the number of identical resistors (2) by the value of the resistance (45 Ω). 

 

 

Example 2: 

 

Find the total resistance of two 16 ohm resistors wired in parallel. 

 

This time, the resistors are wired in parallel parallel. So we use:

 

 

 

You should have gotten 8 Ω. All you had to do was take the value of the common resistor and divided it by two since there are two idential resistors wired in parallel. 

 

Tip: adding a resistor in parallel always lowers the overall resistance. 

 

For this example the resistors have the same number of ohms (i.e. same resistance) but if they didn't then you would want to find the GCF (greatest common factor) to find a common resistor to wire in parallel. For example, if it was a 16 Ω and an 8 Ω wired in parallel, then you would turn the 8 Ω into two 16 Ω 's wired in parallel for a total of three 16 ohm resistors wired in parallel. Then the total resistance would be 5.3 Ω.

 

 

Node Rule  (Kirchhoff's Junction Rule)

 

Another rule we created from the Current and Resistance Lab was the Node Rule. The node rule says that the sum of the currents into any place wires meet has to equal the sum of the currents going out of the node. 

 

 

 

 

Voltage Lab/Voltage Rules

 

Voltage is not the same thing as current. You can think of current as the flow of charges around the circuit. Voltage is the cause of this current. In order for charges to flow, there has to be a difference between the voltages at two different places. You can think of voltages like an "electric pressure" where charges naturally flow from higher electric pressure to lower. 

 

Loop Rule

 

The sum of the voltages in any loop is equal to the voltage of the battery. 

 

Tip: make sure to actually draw a loop when using the loop rule. Only the voltages of resistors/bulbs that are actually present in your specific loop add up to the battery voltage. 

 

For an all series circuit, the loop rule becomes: 

  • In a series, the voltage of the battery is equal to the sum of voltages across the resistors. 

 

For an all parallel circuit, the loop rule becomes: 

  • In a parallel circuit, the voltage of the battery is equal to the voltage of each resistor. This means that, since the voltage of the resistors is all equal in a parallel circuit, any one of their voltages is equal to the voltage of the battery.

 

Battery Voltage

 

Another major rule we discovered in the voltage lab is that the voltage across the battery is always constant.  

 

 

Voltage of Bulbs vs. Voltage of Resistors

 

Light Bulbs and resistors differ in the ways in which their voltage increases as the current through them increase. In both cases the more voltage across the bulb/resistor the greater the current though it (since voltage causes current). However, in a resistor, as the current passing through it increases, the voltage proportionally increases as well. But in light bulbs, as the current passing through it increases, the voltage across the light bulb increases by greater amounts. Another way of thinking about this is that the resistance of a resistor is constant. So if you double the voltage across it the current through it also doubles. However for a bulb the resistance of the bulb actually changes as the voltage/current changes so doubling the voltage increases the current, but it doesn't necessarily double it. 

 

Ohm's Law

 

V = IR

 

We determined Ohm's Law by creating a general math model for the voltage vs. current graph of the resistor which was linear. 

 

Tip: Ohm's law is only applicable if the resistance is constant. Importantly you cannot use Ohm's Law for bulbs instead of resistors, as the resistance of a light bulb is dependent on the current flowing through it.

 

Power

 

From the Energy unit, Power is how quickly energy goes into or out of a system. In general: 

 

 

For an Electric Circuit:

 

P = IV

 

 

Quantitative Circuits

  Use the loop rule, node rule, equivalent resistance rules, and Ohm's Law to solve the following problems.  

 

 

 

How Christmas Lights Work

 

Christmas lights are typically wired in series because it takes less wire, looks better, and reduces the voltage across each bulb. In early Christmas lights if one bulb went out, they all went out, since bulbs in series are dependent of each other. A shunt solves this problem by creating a backup pathway for charge to flow through the bulb when the filament breaks. 

 

Short Circuits

Warning: do not ever just connect a wire directly to both sides of the battery. This is called a short circuit and it is dangerous because the wire will get very hot and burn you. If you see smoke coming from the circuit this means there is a short circuit and that you should disconnect the battery immediately. Another way to short circuit it is by connecting the metal nub to the wire and the battery, and then connecting the wire to the other side. This also heats the wire because the circuit is still running through it, and the resistance of the wire very small, hence a massive current goes through the wire. 

 

TheoryA short circuit is a pathway with very little resistance but still a significant voltage drop across the two sides. This causes the huge current which heats up the wire. 

 

 

Circuit Applications

 

 

Summary

 

 

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