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, but for resistors we deal with the charge per unit of time, the Current. In a circuit the current is not used up as it follows its path, therefore it must be the same throughout all of the resistors. The voltage drop across each resistor is given as:
Slide 4 / 33 Resistors in Parallel and Series The potential difference is not dependent on the path taken, therefore the potential across each resistor in parallel is equal to the net voltage at the junction point. Slide 5 / 33 Resistors in Parallel and Series In a parallel combination the current through each of the resistors is not necessarily the same. If two resistors are placed in a parallel combination and one has a resistance of r and the other has a resistance of 2r. Twice as much current will flow through r, then the resistor of 2r. Slide 6 / 33 1 Current is _______ in a series circuit and voltage is _____ in a parallel circuit. A same, different B different, same C same, same D different, different
Slide 7 / 33 R 1 = 5 # R 2 = 3 # V = 9 V What is the equivalent resistance in this circuit? 8 Ω What is the total current at any spot in the circuit? 1.125 A What is the voltage drop across R 1 ? 5.625 V What is the voltage drop across R 2 ? 3.375 V Slide 8 / 33 R 1 = 3 # R 2 = 6 # V = 18V What is the equivalent resistance in this circuit? 2 Ω What is the voltage at any spot in the circuit? 18 V 6 A What is the current through R 1 ? What is the current through R 2 ? 3 A Slide 9 / 33
Slide 10 / 33 Kirchhoff's Rules 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) Slide 11 / 33 Find the unknowns in the following circuit: R 3 = 2 # I 3 = 10 A ? V 3 = 20 V R 1 = 10 # R 2 = 23 # R 4 = 3 # ? ? ? I 4 = 10 A I 1 = 7 A I 2 = 3 A ? ? ? V 1 = 70 V V 2 = 70 V V 4 = 30 V V = 120 V I 1 = 7 A R 2 = 23.33 Ω V 2 = 70 V V 3 = 20 V I 4 = 10 A V 1 = 70 V V 4 = 30 V Slide 12 / 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.
Slide 13 / 33 d'Arsonval Galvanometer 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. B A C D To measure I net or the current through R 1 you can place an ameter at points A or D. To measure the current in R 2 place the ameter at point B To measure the current in R 3 place the ameter at Point C. Slide 14 / 33 d'Arsonval Galvanometer 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. C D A B F E G To measure the voltage drop across R 1 , connect the voltmeter to points A and B. To measure the voltage drop across R 2 and R 3 , 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. Slide 15 / 33 d'Arsonval Galvanometer A Galvanometer can also be used to measure the resistance of 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. G
Slide 16 / 33 d'Arsonval Galvanometer 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 y x z Slide 17 / 33 d'Arsonval Galvanometer 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. Slide 18 / 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
Slide 19 / 33 R-C Circuits Charging a Capacitor Switch - + X Y Z Immediately after the switch is closed the voltage drop across the resistor is I o R 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 opposes 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: Slide 20 / 33 R-C Circuits Switch + - Charging a Capacitor X Y Z Now we will derive the equations for the charge and current during the charging time. 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. Slide 21 / 33 R-C Circuits Switch + - Charging a Capacitor 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.
Slide 22 / 33 Slide 23 / 33 Switch R-C Circuits + - Charging a Capacitor X Y Z (Charge with respect to time) (Current with respect to time) Slide 24 / 33 R-C Circuits Switch + - Charging a Capacitor X Y Z
Slide 25 / 33 R-C Circuits Charging a Capacitor 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. Slide 26 / 33 R-C Circuits Charging a Capacitor 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. Slide 27 / 33 R-C Circuits Charging a Capacitor 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
Slide 28 / 33 Slide 29 / 33 R-C Circuits Charging a Capacitor Slide 30 / 33 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
Slide 31 / 33 3 The circuit has been connected for a long time. The charge on the plate is A 60 µC B 20 µC C 2 µC D 40 µC E 30 µC Slide 32 / 33 4 The circuit has been connected for a long time. What is the current through the 5 ohm resistor? A 8 A B 6 A C 4 A D 2 A E 0 A Slide 33 / 33 5 A capacitor is placed in series with a resistor and a battery. Which of the following graphs represents the charge on the capacitor as a function of time? C B A D E
Recommend
More recommend
