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19.2. Energy stored in a capacitor
A subsection of Physics, 9702, through 19. Capacitance
Listing 10 of 19 questions
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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A capacitor consists of two metal plates separated by an insulator, as shown in . metal plate insulator metal plate The potential difference between the plates is V. The variation with V of the magnitude of the charge Q on one plate is shown in . V / V Q / mC Explain why the capacitor stores energy but not charge. Use to determine the capacitance of the capacitor, capacitance = μF the loss in energy stored in the capacitor when the potential difference V is reduced from 10.0 V to 7.5 V. energy = mJ Three capacitors X, Y and Z, each of capacitance 10 μF, are connected as shown in . A B Z Y X Initially, the capacitors are uncharged. A potential difference of 12 V is applied between points A and B. Determine the magnitude of the charge on one plate of capacitor X. charge = μC
9702_s11_qp_42
THEORY
2011
Paper 4, Variant 2
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A capacitor consists of two metal plates separated by an insulator, as shown in . metal plate insulator metal plate The potential difference between the plates is V. The variation with V of the magnitude of the charge Q on one plate is shown in . V / V Q / mC Explain why the capacitor stores energy but not charge. Use to determine the capacitance of the capacitor, capacitance = μF the loss in energy stored in the capacitor when the potential difference V is reduced from 10.0 V to 7.5 V. energy = mJ Three capacitors X, Y and Z, each of capacitance 10 μF, are connected as shown in . A B Z Y X Initially, the capacitors are uncharged. A potential difference of 12 V is applied between points A and B. Determine the magnitude of the charge on one plate of capacitor X. charge = μC
9702_s11_qp_43
THEORY
2011
Paper 4, Variant 3
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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 student sets up the circuit shown in to measure the charge on a capacitor C for different values of potential difference across the capacitor. V C meter to measure charge The variation with potential difference V of the charge Q stored on the capacitor is shown in . V / V Q / mC State and explain how indicates that there is a systematic error in the readings of one of the meters. Use to determine the capacitance, in μF, of capacitor C. capacitance = μF Use your answer in to determine the additional energy stored in the capacitor C when the potential difference across it is increased from 6.0 V to 9.0 V. energy = J
9702_s16_qp_41
THEORY
2016
Paper 4, Variant 1
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A student sets up the circuit shown in to measure the charge on a capacitor C for different values of potential difference across the capacitor. V C meter to measure charge The variation with potential difference V of the charge Q stored on the capacitor is shown in . V / V Q / mC State and explain how indicates that there is a systematic error in the readings of one of the meters. Use to determine the capacitance, in μF, of capacitor C. capacitance = μF Use your answer in to determine the additional energy stored in the capacitor C when the potential difference across it is increased from 6.0 V to 9.0 V. energy = J
9702_s16_qp_43
THEORY
2016
Paper 4, Variant 3
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Questions Discovered
19