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AP Physics C - E & M Direct Current Circuits 2015-12-05 - - PDF document
AP Physics C - E & M Direct Current Circuits 2015-12-05 - - PDF document
Slide 1 / 33 Slide 2 / 33 AP Physics C - E & M Direct Current Circuits 2015-12-05 www.njctl.org Slide 3 / 33 Resistors in Parallel and Series For capacitors in circuits we always focused on how much charge was transferred to the plates,
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R1 = 5# R2 = 3# V = 9 V What is the equivalent resistance in this circuit? What is the total current at any spot in the circuit? What is the voltage drop across R
1?
What is the voltage drop across R
2?
8 Ω 1.125 A 5.625 V 3.375 V
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R1 = 3# R2 = 6# V = 18V What is the equivalent resistance in this circuit? What is the voltage at any spot in the circuit? What is the current through R1? What is the current through R2? 2 Ω 18 V 6 A 3 A
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Kirchhoff's Loop rule: The algebraic sum of the potential differences in any loop, including those associated with emfs and those of resistive elements must equal zero. (Kirchhoff's Loop Rule)
Kirchhoff's Rules Slide 10 / 33
Find the unknowns in the following circuit: V = 120 V R1 = 10 # I1 = 7 A V1 = 70 V R3 = 2 # I3 = 10 A V3 = 20 V R4 = 3 # I4 = 10 A V4 = 30 V R2 = 23 # I2 = 3 A V2 = 70 V ? ? ? ? ? ? ? I1 = 7 A I4 = 10 A R2 = 23.33 Ω V1 = 70 V V2 = 70 V V3 = 20 V V4 = 30 V
Slide 11 / 33 d'Arsonval Galvanometer
A d'Arsonval Galvnometer can be used to determine the current, electric potential, and the resistance based off of how electric current is related to magnetic fields. A d'Arsonval Galvnometer is comprised of a coil of fine wire that is placed in a permanent magnetic field. A spring is attached to the coil and when a current is present the magnetic field exerts a torque on the coil.
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An ammeter is a device used to measure the magnitude of the current in a circuit. Since the current is not used up in the circuit, the meter has to be placed in series with whatever current you are trying to measure. A B C D To measure Inet or the current through R1 you can place an ameter at points A or D. To measure the current in R2 place the ameter at point B To measure the current in R3 place the ameter at Point C.
d'Arsonval Galvanometer Slide 13 / 33
A voltmeter is a device used to measure the potential difference between two points. When talking about parallel combinations we said that the voltage drop across each branch is the same. To measure the voltage drop across an element in the circuit you have to place the voltmeter in parallel.
A B C D E F G
To measure the voltage drop across R1, connect the voltmeter to points A and B. To measure the voltage drop across R2 and R3, connect the voltmeter to points C and D or points E and F. To measure the voltage drop across the entire circuit, connect the voltmeter to points A and G.
d'Arsonval Galvanometer Slide 14 / 33
G A Galvanometer can also be used to measure the resistance
- f an unknown resistor, this is called an Ohmmeter.
Instead of just using a Galvanometer, it also requires a flashlight battery of known #, and a variable resistor. In doing so, you can determine the resistance because you have determined the current or the meter could have been calibrated to read what the resistance is.
d'Arsonval Galvanometer Slide 15 / 33
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Unlike a voltmeter, a potentiometer does not draw any current from the source. It works on the principal of balancing a known potential difference with the unknown by using Kirchhoff's Loop
- Rules. A potentiometer is comprised of a Galvanometer, a
variable resistor, and a battery with a known #. G x y z
d'Arsonval Galvanometer Slide 16 / 33
Any meter can be used to measure currents and voltages that are larger then there capacities. By placing a shunt resistor in parallel to the ammeter, we know that since it is a parallel connection part of the current will flow through the ammeter and the rest will flow through the resistor. By placing a shunt resistor in series with a voltmeter we can find the voltage drop when it is out of the meter's range.
d'Arsonval Galvanometer Slide 17 / 33 R-C Circuits
Up till now we never talked about the time it took to charge or discharge a capacitor, before we also mentioned that initially it was uncharged, that it had been completely charged, or asked after a long time what was the charge on the capacitor. To deal with the time in between we will use the simple circuit shown below to derive equations for charging and discharging a capacitor. +
- Switch
X Y Z
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+
- Switch
X Y Z
Immediately after the switch is closed the voltage drop across the resistor is IoR and the potential difference across the capacitor is
- zero. After sometime the current in the circuit decreases because
the capacitor is charging and producing an electric field which
- pposes the one generated by the battery. The potential
difference across the resistor is now iR and the potential difference of the capacitor is Q/C. After the capacitor has been completely charged the current through the circuit is zero, and the charge on the capacitor's plates is:
R-C Circuits Charging a Capacitor Slide 19 / 33
Now we will derive the equations for the charge and current during the charging time. + -
Switch X Y Z
Now we have run into a problem in our equation because we have two unknown variables, current and charge, but what is current? Current is the rate of charge.
R-C Circuits Charging a Capacitor Slide 20 / 33
+ -
Switch X Y Z
Now it is time to integrate both of these expressions. Initially the charge was zero and our time was also zero. Now since we are still talking about a case in between the charging time we don't integrate to the max value of Q, instead to q, an intermediate value.
R-C Circuits Charging a Capacitor Slide 21 / 33
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+ -
Switch X Y Z
(Charge with respect to time) (Current with respect to time)
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+ -
Switch X Y Z
R-C Circuits Charging a Capacitor Slide 24 / 33
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In the equations we just solved for on the previous side they are both dependent on RC. The product of RC is called the Time Constant and is denoted by . If is small then the charging time of the capacitor is short, and if it is greater the charging time is also greater. This reasoning is rather intuitive because if the resistance changes the current, the rate at which the charge flows, either increases or decreases and by changing the capacitance it can hold either more or less charge then originally.
R-C Circuits Charging a Capacitor Slide 25 / 33
We will use the following circuit and the givens to derive equations for when a capacitor is discharging.
Switch X Y Z
In this example we have a capacitor charged to its max value of Q, and initially the switch is open. After the switch is closed the capacitor will begin discharging with a max current of I. The current however is negative because it results in a decrease in the charge on the capacitor. After a long time the charge on the capacitor will be zero and the current will also drop down to zero. Now lets talk about the time in between when the switch was closed until everything dropped to zero.
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Once again we will apply Kirchhoff's Loop Rule to derive the equation for the charge on the capacitor with respect to time. In this scenario the capacitor is acting like a source, its is Q/C and the voltage drop across the resistor is given as iR.
because the charge on the capacitor is decreasing
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2 The circuit is closed initially. What is the current through the 5 ohm resistor? A 0 A B 2 A C 4 A D 6 A E 8 A
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