Charging an RC Circuit

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Discharging an RC Circuit

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2013 Free Response Question 2

c In a lab, you set up a circuit that contains a capacitor C, a resistor R, a switch S, and a power supply, as shown in the diagram above. The capacitor is initially uncharged. The switch, which is initially open, can be moved to positions A or B. (a) i. Indicate the position to which the switch should be moved to charge the capacitor. ii. On the diagram, draw a voltmeter that is properly connected to the circuit in a manner that will allow the voltage to be measured across the capacitor. After a long time you move the switch to discharge the capacitor, and your lab partner starts a stopwatch. You collect the following measurements of the voltage across the capacitor at various times. 6 252 18 74 30 33 42 10 54 6 You wish to determine the time constant T of the circuit from the slope of a linear graph. (b) . Indicate two quantities you would plot to obtain a linear graph. ii. Use the remaining rows in the table above, as needed, to record any quantities that you indicated that are not given. Label each row you use and include units.

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(c) On the axes below, graph the data from the table that will produce a linear relationship. Clearly scale and label all axes including units, if appropriate. Draw a straight line that best fits your data points. cru -J \_J 4 4.-4 4. 4 4. 4. (d) From your line in part (c), obtain the value of the time constant T of the circuit. (e) . In the experiment, the capacitor C had a capacitance of 1.50 gF. Calculate an experimental value for the resistance R. ii. On the axes in part (c), use a dashed line to sketch a possible graph if the capacitance was greater than 1.50 gF but the resistance R was the same. Justify your answer.

学 ト 0 ・ 、 ← 。 》 ← 2 ← 0 ( に

2012 Free Response Question 2

0.02 ml Paper Strip A physics student wishes to measure the resistivity of slightly conductive paper that has a thickness of 1.0 x 10-4 m . The student cuts a sheet of the conductive paper into strips of width 0.02 m and varying lengths, making five resistors labeled RI to R5. Using an ohmmeter, the student measures the resistance of each strip, as shown above. The data are recorded below. Resistor Length (m) Resistance ( Q ) RI 0.020 80,000 0.040 180,000 0.060 260,000 0.080 370,000 0.100 440,000 (a) Use the grid below to plot a linear graph of the data points from which the resistivity of the paper can be determined. Include labels and scales for both axes. Draw the straight line that best represents the data. (b) Using the graph, calculate the resistivity of the paper.

9

Capacitor R4 Switch Battery The student uses resistors R4 and R5 to build a circuit using wire, a 1.5 V battery, an uncharged 10 BF capacitor, and an open switch, as shown above. (c) Calculate the time constant of the circuit. (d) At time t = 0, the student closes the switch. On the axes below, sketch the magnitude of the voltage Vc across the capacitor and the magnitudes of the voltages VR4 and VR5 across each resistor as functions of time t. Clearly label each curve according to the circuit element it represents. On the axes, explicitly label any intercepts, asymptotes, maxima, or minima with values or expressions, as appropriate. Time t

t'310

2007 Free Response Question 1

Switch R = 550 Q C = 4000gF A student sets up the circuit above in the lab. The values of the resistance and capacitance are as shown, but the constant voltage E delivered by the ideal battery is unknown. At time t = 0, the capacitor is uncharged and the student closes the switch. The current as a function of time is measured using a computer system, and the following graph is obtained. 2.5 2.0 1.0 0.5 O 2 4 6 lime (s) 8 10 Using the data above, calculate the battery voltage E . (a) (b Calculate the voltage across the capacitor at time t = 4.0 s. Calculate the charge on the capacitor at t = 4.0 s. (c)

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(d) On the axes below, sketch a graph of the charge on the capacitor as a function of time. 10 Time (s) (e) Calculate the power being dissipated as heat in the resistor at t = 4.0 s. (f) The capacitor is now discharged, its dielectric of constant K = 1 is replaced by a dielectric of constant K = 3 , and the procedure is repeated. Is the amount of charge on one plate of the capacitor at t = 4.0 s now greater than, less than, or the same as before? Justify your answer. Greater than Less than The same

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2006 Free Response Question 2

c The circuit above contains a capacitor of capacitance C, a power supply of emf e , two resistors of resistances RI and R2 , and two switches, Sl and S2 . Initially, the capacitor is uncharged and both switches are open. Switch Sl then gets closed at time t = O. (a) Write a differential equation that can be solved to obtain the charge on the capacitor as a function of time t. (b) Solve the differential equation in part (a) to determine the charge on the capacitor as a function of time t. Numerical values for the components are given as follows: e = 12 v C = 0.060 F RI = = 4700 Q (c) Determine the time at which the capacitor has a voltage 4.0 V across it. After switch Sl has been closed for a long time, switch S2 gets closed at a new time t = O.

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(c) Determine the time at which the capacitor has a voltage 4.0 V across it. After switch Sl has been closed for a long time, switch S2 gets closed at a new time t = O. (d) On the axes below, sketch graphs of the current Il in RI versus time and of the current 12 in R2 versus time, beginning when switch S2 is closed at new time t = O. Clearly label which graph is Il and which is 12 . Current Time

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2003 Response Question 2

In the laboratory, you connect a resistor and a capacitor with unknown values in series with a battery of emf E = 12 V . You include a switch in the circuit. When the switch is closed at time t = 0, the circuit is completed, and you measure the current through the resistor as a function of time as plotted below. 0.010 0.005 4 8 12 16 e e-t/4 A data-fitting program finds that the current decays according to the equation i(t) = (a) Using common symbols for the battery, the resistor, the capacitor, and the switch, draw the circuit that you constructed. Show the circuit before the switch is closed and include whatever other devices you need to measure the current through the resistor to obtain the above plot. Label each component in your diagram. (b) Having obtained the curve shown above, determine the value of the resistor that you placed in this circuit. (c) What capacitance did you insert in the circuit to give the result above?

ΙΙ V = > ΙΙOΟ-η- ΙΙΦΠ

You are now asked to reconnect the circuit with a new switch in such a way as to charge and discharge the capacitor. When the switch in the circuit is in position A, the capacitor is charging; and when the switch is in position B, the capacitor is discharging, as represented by the graph below of voltage Vc across the capacitor as a function of time. Vc(V) Switch at A Charging 12 6 4 8 12 Switch at B Discharging 16 20 24 28 32 (d) Draw a schematic diagram of the RC circuit that you constructed that would produce the graph above. Clearly indicate switch positions A and B on your circuit diagram and include whatever other devices you need to measure the voltage across the capacitor to obtain the above plot. Label each component in your diagram.

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