21.2. Rectification and smoothing
A subsection of Physics, 9702, through 21. Alternating currents
Listing 10 of 23 questions
Use An ideal transformer has 5000 turns on its primary coil. It is to be used to convert a mains supply of 230 V r.m.s. to an alternating voltage having a peak value of 9.0 V. Calculate the number of turns on the secondary coil. number = ……………………………… The output from the transformer is to be full-wave rectified. shows part of the rectifier circuit. A B R On , draw diode symbols to complete the diagram of the rectifier such that terminal A of the resistor R is positive with respect to terminal B, the symbol for a capacitor connected to provide smoothing of the potential difference across the resistor R. Examiner’s Use shows the variation with time t of the smoothed potential difference V across the resistor R. V t1 t3 t4 t t2 State the interval of time during which the capacitor is being charged from the transformer. from time ………… to time …………… The resistance of the resistor R is doubled. On , sketch the variation with time t of the potential difference V across the resistor.
9702_s07_qp_4
THEORY
2007
Paper 4, Variant 0
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shows four diodes and a load resistor of resistance 1.2 kΩ, connected in a circuit that is used to produce rectification of an alternating voltage. X VIN VOUT 1.2 kΩ Y P Q State what is meant by rectification. State the type of rectification produced by the circuit in . A sinusoidal alternating voltage VIN is applied across the input terminals X and Y. The variation with time t of VIN is given by the equation VIN = 6.0 sin 25πt where VIN is in volts and t is in seconds. On , label the output terminals P and Q with the appropriate symbols to indicate the polarity of the output voltage VOUT. The magnitude of the output voltage VOUT varies with t as shown in . VOUT / V t / s On , label both of the axes with the correct scales. Use the space below for any working that you need. The output voltage in is smoothed by adding a capacitor to the circuit in . The difference between the maximum and minimum values of the smoothed output voltage is 10% of the peak voltage. On , draw the circuit symbol for a capacitor showing the capacitor correctly connected into the circuit. On , sketch the variation with t of the smoothed output voltage. Calculate the capacitance C of the capacitor. C = F
9702_s22_qp_41
THEORY
2022
Paper 4, Variant 1
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shows four diodes and a load resistor of resistance 1.2 kΩ, connected in a circuit that is used to produce rectification of an alternating voltage. X VIN VOUT 1.2 kΩ Y P Q State what is meant by rectification. State the type of rectification produced by the circuit in . A sinusoidal alternating voltage VIN is applied across the input terminals X and Y. The variation with time t of VIN is given by the equation VIN = 6.0 sin 25πt where VIN is in volts and t is in seconds. On , label the output terminals P and Q with the appropriate symbols to indicate the polarity of the output voltage VOUT. The magnitude of the output voltage VOUT varies with t as shown in . VOUT / V t / s On , label both of the axes with the correct scales. Use the space below for any working that you need. The output voltage in is smoothed by adding a capacitor to the circuit in . The difference between the maximum and minimum values of the smoothed output voltage is 10% of the peak voltage. On , draw the circuit symbol for a capacitor showing the capacitor correctly connected into the circuit. On , sketch the variation with t of the smoothed output voltage. Calculate the capacitance C of the capacitor. C = F
9702_s22_qp_43
THEORY
2022
Paper 4, Variant 3
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Four diodes are used in a bridge rectifier circuit to produce rectification of a sinusoidal a.c. input voltage VIN. shows part of the circuit, but three of the diodes are missing. VIN VOUT R The p.d. across the load resistor R is the output p.d. VOUT of the bridge rectifier. State the name of the type of rectification produced by a bridge rectifier. Complete by drawing the three missing diodes, correctly connected. On , draw an arrow to indicate the direction of the current in resistor R. VIN has amplitude V0 and period T. shows the variation with time t of VIN. VIN 0.5T 1.0T 1.5T 2.0T t –V0 V0 On , sketch the variation of VOUT with t between t = 0 and t = 2.0T. VOUT 0.5T 1.0T 1.5T 2.0T t –V0 V0 The power dissipated in the resistor is P. On , sketch the variation of P with t between t = 0 and t = 2.0T. P 0.5T 1.0T 1.5T 2.0T t Suggest, with a reason, how the root-mean-square (r.m.s.) value of VOUT compares with the r.m.s. value of VIN.
9702_s23_qp_42
THEORY
2023
Paper 4, Variant 2
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A sinusoidal alternating voltage is to be rectified. Suggest one advantage of full-wave rectification as compared with half-wave rectification. The rectification is produced using the circuit of . A B R All the diodes may be considered to be ideal. The variation with time t of the alternating voltage applied to the circuit is shown in and in . voltage t voltage t On the axes of , draw a graph to show the variation with time t of the potential difference across diode A. On the axes of , draw a graph to show the variation with time t of the potential difference across diode B. On , draw the symbol for a capacitor, connected into the circuit so as to provide smoothing. shows the variation with time t of the smoothed potential difference across the resistor R in . potential difference t 1. State how the amount of smoothing may be increased. 2. On , draw the variation with time t of the potential difference across resistor R for increased smoothing.
9702_w09_qp_41
THEORY
2009
Paper 4, Variant 1
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The circuit for a full-wave rectifier using four ideal diodes is shown in . Y B A R X input A resistor R is connected across the output AB of the rectifier. On , draw a circle around any diodes that conduct when the terminal X of the input is positive with respect to terminal Y, label the positive (+) and the negative (–) terminals of the output AB. The variation with time t of the potential difference V across the input XY is given by the expression V = 5.6 sin 380t where V is measured in volts and t is measured in seconds. The variation with time t of the rectified potential difference across the resistor R is shown in . rectified potential difference / V t2 t t1 Use the expression for the input potential difference V, or otherwise, to determine the root-mean-square (r.m.s.) potential difference Vr.m.s. of the input, Vr.m.s. = V the number of times per second that the rectified potential difference at the output reaches a peak value. number = A capacitor is now connected between the terminals AB of the output. The capacitor reduces the variation (the ripple) in the output to 1.6 V. On , sketch the variation with time t of the smoothed output voltage for time t = t1 to time t = t2. Suggest and explain the effect, if any, on the mean power dissipation in resistor R when the capacitor is connected between terminals AB.
9702_w17_qp_42
THEORY
2017
Paper 4, Variant 2
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State what is meant by rectification of an alternating voltage. State the difference between half-wave rectification and full-wave rectification. Complete to show a circuit that produces half-wave rectification of an alternating input voltage VIN to produce output voltage VOUT across the resistor R. VIN VOUT R C State the purpose of the capacitor C in the circuit of . The input voltage VIN in is a square wave. shows the variation of VIN with time t. –12 VIN / V +12 0.01 0.02 t / s 0.03 0.04 shows the variation of VOUT with t. VOUT / V 0.01 0.02 t / s 0.03 0.04 The maximum energy stored in the capacitor is 0.041 J. Show that the capacitance of C is 570 μF. Determine the resistance of R. resistance = Ω
9702_w24_qp_41
THEORY
2024
Paper 4, Variant 1
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State what is meant by rectification of an alternating voltage. State the difference between half-wave rectification and full-wave rectification. Complete to show a circuit that produces half-wave rectification of an alternating input voltage VIN to produce output voltage VOUT across the resistor R. VIN VOUT R C State the purpose of the capacitor C in the circuit of . The input voltage VIN in is a square wave. shows the variation of VIN with time t. –12 VIN / V +12 0.01 0.02 t / s 0.03 0.04 shows the variation of VOUT with t. VOUT / V 0.01 0.02 t / s 0.03 0.04 The maximum energy stored in the capacitor is 0.041 J. Show that the capacitance of C is 570 μF. Determine the resistance of R. resistance = Ω
9702_w24_qp_43
THEORY
2024
Paper 4, Variant 3
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The output potential difference (p.d.) of an alternating power supply is represented by V = 320 sin(100 πt) where V is the p.d. in volts and t is the time in seconds. Determine the root-mean-square (r.m.s.) p.d. of the power supply. r.m.s. p.d. = V Determine the period T of the output. T = s The power supply is connected to resistor R and a diode in the circuit shown in . V R State the name of the type of rectification produced by the diode in . On sketch the variation with time t of the p.d. VR across R from time t = 0 to time t = 40 ms. –400 –300 –200 –100 V / V t / ms On , draw the symbol for a component that may be connected to produce smoothing of VR.
9702_m21_qp_42
THEORY
2021
Paper 4, Variant 2
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Questions Discovered
23