19. Capacitance
A section of Physics, 9702
Listing 10 of 66 questions
Define the capacitance of a parallel‑plate capacitor. An initially uncharged capacitor X, of capacitance C, is gradually charged so that the final potential difference (p.d.) between its plates is V and the final charge is Q. On , sketch the variation of charge with p.d. for capacitor X as the p.d. increases from 0 to V. charge Q V p.d. Determine an expression, in terms of Q and V, for the work W done on capacitor X during the charging process. Explain your reasoning. W = Another capacitor Y is initially uncharged. The fully charged capacitor X in is now connected to capacitor Y, as shown in . Y X The capacitance of capacitor Y is 3C. Complete Table 7.1 to show expressions, in terms of Q and V, for the final p.d.s across, and the final charges on, the two capacitors. Use the space below for any working that you need. Table 7.1 X Y final p.d. final charge State whether the total energy stored in the two capacitors is less than, the same as, or greater than the energy initially stored in capacitor X.
9702_w24_qp_42
THEORY
2024
Paper 4, Variant 2
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The variation with potential difference V of the charge Q on one of the plates of a capacitor is shown in . V / V Q / 10–4 C 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 The capacitor is connected to an 8.0 V power supply and two resistors R and S as shown in . R 25 kΩ S 220 kΩ 8.0 V X Y The resistance of R is 25 kΩ and the resistance of S is 220 kΩ. The switch can be in either position X or position Y. The switch is in position X so that the capacitor is fully charged. Calculate the energy E stored in the capacitor. E = J The switch is now moved to position Y. Show that the time constant of the discharge circuit is 3.3 s. The fully charged capacitor in stores energy E. Determine the time t taken for the stored energy to decrease from E to E / 9. t = s A second identical capacitor is connected in parallel with the first capacitor. State and explain the change, if any, to the time constant of the discharge circuit.
9702_m22_qp_42
THEORY
2022
Paper 4, Variant 2
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A capacitor, a battery of electromotive force (e.m.f.) 12 V, a resistor R and a two-way switch are connected in the circuit shown in . 12 V T S R The switch is initially in position S. When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time t after the switch is moved the charge on the capacitor is Q. The variation with t of ln (Q / μC) is shown in . t / s ln (Q /μC) Show that the capacitance of the capacitor is 1.5 μF. Determine the resistance of R. resistance = Ω Calculate the energy stored in the capacitor at time t = 0. energy = J A second identical resistor is now connected in parallel with R. The switch is initially in position S. When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time t after the switch is moved the charge on the capacitor is Q. On , sketch a line to show the variation of ln (Q / μC) with t between time t = 0 and time t = 5.0 s.
9702_m23_qp_42
THEORY
2023
Paper 4, Variant 2
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An uncharged capacitor is connected in series with a battery, a switch and a resistor, as shown in . 9.0 V 4700 +F The battery has e.m.f. 9.0 V and negligible internal resistance. The capacitance of the capacitor is 4700 μF. The switch is closed at time t = 0. During the time interval t = 0 to t = 4.0 s, the charge passing through the resistor is 22 mC. Calculate the energy transfer in the battery during the time interval t = 0 to t = 4.0 s. energy transfer = J Determine, for the capacitor at time t = 4.0 s, 1. the potential difference V across the capacitor, V = V 2. the energy stored in the capacitor. energy = J Suggest why your answers in and part 2 are different.
9702_s14_qp_41
THEORY
2014
Paper 4, Variant 1
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An uncharged capacitor is connected in series with a battery, a switch and a resistor, as shown in . 9.0 V 4700 +F The battery has e.m.f. 9.0 V and negligible internal resistance. The capacitance of the capacitor is 4700 μF. The switch is closed at time t = 0. During the time interval t = 0 to t = 4.0 s, the charge passing through the resistor is 22 mC. Calculate the energy transfer in the battery during the time interval t = 0 to t = 4.0 s. energy transfer = J Determine, for the capacitor at time t = 4.0 s, 1. the potential difference V across the capacitor, V = V 2. the energy stored in the capacitor. energy = J Suggest why your answers in and part 2 are different.
9702_s14_qp_43
THEORY
2014
Paper 4, Variant 3
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A capacitor consists of two parallel metal plates, separated by an insulator, as shown in . metal plates insulator Suggest why, when the capacitor is connected across the terminals of a battery, the capacitor stores energy, not charge. Define the capacitance of the capacitor. The capacitor is charged so that the potential difference between its plates is V0. The capacitor is then connected across a resistor for a short time. It is then disconnected. The energy stored in the capacitor is reduced to 16 1 of its initial value. Determine, in terms of V0, the potential difference across the capacitor. potential difference =
9702_s17_qp_42
THEORY
2017
Paper 4, Variant 2
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An alternating supply of frequency 50 Hz and having an output of 6.0 V r.m.s. is to be rectified so as to provide direct current for a resistor R. The circuit of is used. The diode is ideal. The Y-plates of a cathode-ray oscilloscope (c.r.o.) are connected between points A and B. Calculate the maximum potential difference across the diode during one cycle. potential difference = ………………………… V State the potential difference across R when the diode has maximum potential difference across it. Give a reason for your answer. Use A 50 Hz 6.0 V r.m.s B R [T The Y-plate sensitivity of the c.r.o. is set at 2.0 V cm–1 and the time-base at 5.0 ms cm–1. On , draw the waveform that is seen on the screen of the c.r.o. A capacitor of capacitance 180 µF is connected into the circuit to provide smoothing of the potential difference across the resistor R. On , show the position of the capacitor in the circuit. Calculate the energy stored in the fully-charged capacitor. energy = ………………………… J 1.0 cm 1.0 cm During discharge, the potential difference across the capacitor falls to 0.43 V0, where V0 is the maximum potential difference across the capacitor. Calculate the fraction of the total energy that remains in the capacitor after the discharge. fraction = …………………………
9702_w06_qp_4
THEORY
2006
Paper 4, Variant 0
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A capacitor of capacitance 470 μF is connected to a battery of electromotive force (e.m.f.) 24 V in the circuit of . V 24 V 470 μF S X Y 5.6 kΩ 5.6 kΩ P Q The two-way switch S is initially at position X. P and Q are identical long straight wires, each with a resistance of 5.6 kΩ. These wires are placed near to, and parallel to, each other. Wire Q is connected to a voltmeter. At time t = 0, switch S is moved to position Y so that the capacitor discharges through wire P. Calculate the charge Q0 on the capacitor at time t = 0. Q0 = C Calculate the current I0 in wire P at time t = 0. I0 = A Calculate the time constant τ of the discharge circuit. τ = s On , sketch a line to show the variation with t of the current I in wire P as the capacitor discharges. I I0 t Explain why there is an induced e.m.f. across wire Q during the discharge of the capacitor. On , sketch a line to suggest the variation with t of the voltmeter reading V. t V
9702_w22_qp_41
THEORY
2022
Paper 4, Variant 1
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Questions Discovered
66