21.1. Characteristics of alternating currents
A subsection of Physics, 9702, through 21. Alternating currents
Listing 10 of 32 questions
A circuit contains a power supply that provides a sinusoidal alternating input voltage VIN. There is an output voltage VOUT across a load resistor R, as shown in . VIN VOUT R State the purpose of the circuit in . shows the variation of VOUT with time t. 0.02 0.04 0.06 0.08 t / s VOUT / V The load resistor R has a resistance of 370 Ω. Show that the maximum power dissipated in R is 0.22 W. On , sketch the variation with t of the power P dissipated in R. 0.02 0.04 0.06 0.08 0.2 0.4 t / s P / W Calculate the mean power dissipated in R. mean power = W The circuit of is disconnected, and R is connected directly across the power supply. Explain, without calculation, how the mean power now dissipated in R compares with the answer in .
9702_s24_qp_41
THEORY
2024
Paper 4, Variant 1
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A circuit contains a power supply that provides a sinusoidal alternating input voltage VIN. There is an output voltage VOUT across a load resistor R, as shown in . VIN VOUT R State the purpose of the circuit in . shows the variation of VOUT with time t. 0.02 0.04 0.06 0.08 t / s VOUT / V The load resistor R has a resistance of 370 Ω. Show that the maximum power dissipated in R is 0.22 W. On , sketch the variation with t of the power P dissipated in R. 0.02 0.04 0.06 0.08 0.2 0.4 t / s P / W Calculate the mean power dissipated in R. mean power = W The circuit of is disconnected, and R is connected directly across the power supply. Explain, without calculation, how the mean power now dissipated in R compares with the answer in .
9702_s24_qp_43
THEORY
2024
Paper 4, Variant 3
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A student is using a power supply that produces a sinusoidal output. The meters on the supply show that the output voltage V has a root-mean-square (r.m.s.) value of 14 V with a frequency of 750 Hz. The variation with time t of the output voltage V may be represented by the expression V = V0 sinωt. Determine the value of V0, V0 = V ω. ω = rad s−1 A capacitor with a large capacitance is connected across the terminals of the supply. Suggest and explain why this may lead to a large current from the supply.
9702_w15_qp_43
THEORY
2015
Paper 4, Variant 3
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A sinusoidal alternating voltage has a root-mean-square (r.m.s.) potential difference (p.d.) of 4.2 V and a frequency of 50 kHz. The alternating voltage is applied across a resistor of resistance 760 Ω. By considering the peak voltage, show that the maximum power dissipated by the resistor is 46 mW. On , draw a smooth curve to show how the power P dissipated in the resistor varies with time t between t = 0 and t = 40 μs. Assume that P = 0 when t = 0. P / mW t / μs Use your line in to explain why the mean power dissipated in the resistor is 23 mW. The alternating voltage in is now applied to a piezoelectric crystal in air. Explain what happens to the air surrounding the crystal. A second piezoelectric crystal is placed in the air near to the first crystal. Explain the effect of the surrounding air in on the second crystal.
9702_w22_qp_41
THEORY
2022
Paper 4, Variant 1
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A sinusoidal alternating voltage has a root-mean-square (r.m.s.) potential difference (p.d.) of 4.2 V and a frequency of 50 kHz. The alternating voltage is applied across a resistor of resistance 760 Ω. By considering the peak voltage, show that the maximum power dissipated by the resistor is 46 mW. On , draw a smooth curve to show how the power P dissipated in the resistor varies with time t between t = 0 and t = 40 μs. Assume that P = 0 when t = 0. P / mW t / μs Use your line in to explain why the mean power dissipated in the resistor is 23 mW. The alternating voltage in is now applied to a piezoelectric crystal in air. Explain what happens to the air surrounding the crystal. A second piezoelectric crystal is placed in the air near to the first crystal. Explain the effect of the surrounding air in on the second crystal.
9702_w22_qp_43
THEORY
2022
Paper 4, Variant 3
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A varying current I passes through a resistor of resistance R in the circuit shown in . R I shows the variation with time t of I. I I0 2I0 3I0 –I0 –2I0 –3I0 0.5 T 1.0 T 1.5 T 2.0 T t The current has magnitude 2I0 when it is in the positive direction and I0 when it is in the negative direction. The period of the variation of the current is T. Determine expressions, in terms of I0 and R, for the power P dissipated in the resistor for the times when: the current is in the negative direction P = the current is in the positive direction. P = On , sketch the variation of P with t between t = 0 and t = 2.0T. Label the power axis with an appropriate scale. P 0.5 T 1.0 T 1.5 T 2.0 T t Use your answer in to determine an expression, in terms of I0 and R, for: the mean power 〈P 〉 in the resistor 〈P 〉 = the root-mean-square (r.m.s.) current Ir.m.s. in the resistor. Ir.m.s. =
9702_w23_qp_41
THEORY
2023
Paper 4, Variant 1
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An electron in a metal rod moves randomly about a mean position. When an alternating voltage is applied to the ends of the rod, the mean position can be considered to oscillate with simple harmonic motion along the axis of the rod. shows the variation with time t of the displacement x of the mean position from a fixed point on the axis of the rod. 0.1 0.2 0.3 0.4 x / 10–15 m t / μs Determine the amplitude of the oscillations. amplitude = m Determine the angular frequency of the oscillations. angular frequency = rad s–1 Use your answers in and to show that the maximum drift speed v0 of the electron is 1.1 × 10–7 m s–1. The rod has a cross-sectional area of 4.3 cm2 and contains a number density of conduction electrons (charge carriers) of 8.5 × 1028 m–3. All of the conduction electrons in the rod may be assumed to be oscillating in phase with, and with the same amplitude as, the oscillation shown in . Use the information in to calculate the magnitude I0 of the maximum current in the rod. I0 = A On , sketch the variation of the current I in the rod with time t between t = 0 and t = 0.40 μs. I I0 –I0 0.1 0.2 0.3 0.4 t / μs Use your answers in and to determine an expression for I in terms of t, where I is in A and t is in s. I = Determine the root-mean-square (r.m.s.) current in the rod. r.m.s. current = A
9702_w23_qp_42
THEORY
2023
Paper 4, Variant 2
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A varying current I passes through a resistor of resistance R in the circuit shown in . R I shows the variation with time t of I. I I0 2I0 3I0 –I0 –2I0 –3I0 0.5 T 1.0 T 1.5 T 2.0 T t The current has magnitude 2I0 when it is in the positive direction and I0 when it is in the negative direction. The period of the variation of the current is T. Determine expressions, in terms of I0 and R, for the power P dissipated in the resistor for the times when: the current is in the negative direction P = the current is in the positive direction. P = On , sketch the variation of P with t between t = 0 and t = 2.0T. Label the power axis with an appropriate scale. P 0.5 T 1.0 T 1.5 T 2.0 T t Use your answer in to determine an expression, in terms of I0 and R, for: the mean power 〈P 〉 in the resistor 〈P 〉 = the root-mean-square (r.m.s.) current Ir.m.s. in the resistor. Ir.m.s. =
9702_w23_qp_43
THEORY
2023
Paper 4, Variant 3
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Questions Discovered
32