Question 6
6
A sinusoidal alternating voltage supply is connected to a bridge rectifier consisting of four ideal diodes. The output of the rectifier is connected to a resistor R and a capacitor C as shown in Fig. 6.1. The function of C is to provide some smoothing to the potential difference across R . The variation with time t of the potential difference V across the resistor R is shown in Fig. 6.2.
structured5 marks
Question 6(b)
6(b)
The capacitor C has capacitance \(5.0 \mu \mathrm{~F}\). For a single discharge of the capacitor through the resistor R, use Fig. 6.2 to
structured5 marks
Question 6(b)(i)
6(b)(i)
determine the change in potential difference,
Mediumstructured1 marks
Answer
change \(=4.0-2.4=1.6 \mathrm{~V}\)
Question 6(b)(ii)
6(b)(ii)
determine the change in charge on each plate of the capacitor, C
Mediumstructured2 marks
Answer
C1
Question 6(b)(iii)
6(b)(iii)
show that the average current in the resistor is \(1.1 \times 10^{-3} \mathrm{~A}\).
Mediumstructured2 marks
Answer
C1
Question 5
5
A sinusoidal alternating potential difference (p.d.) from a supply is rectified using a single diode. The variation with time t of the rectified potential difference V is shown in Fig. 5.1.
structured7 marks
Question 5(a)
5(a)
1 marks
Question 5(a)(ii)
5(a)(ii)
State the type of rectification shown in Fig. 5.1.
Easystructured1 marks
Answer
half-wave (rectification) B1
Question 5(b)
5(b)
The alternating potential difference is rectified and smoothed using the circuit in Fig. 5.2. The capacitor has capacitance C of \(85 \mu \mathrm{~F}\) and the resistor has resistance R. The effect of the capacitor and the resistor is to produce a smoothed output potential difference \(V_{\text {OUT }}\). The difference between maximum and minimum values of \(V_{\text {OUT }}\) is 2.0 V .
structured6 marks
Question 5(b)(i)
5(b)(i)
On Fig. 5.1, draw a line to show \(V_{\text {OUT }}\) between times \(t=1.0 \mathrm{~ms}\) and \(t=5.0 \mathrm{~ms}\).
Mediumstructured3 marks
Answer
line from peak at \(t=1.0 \mathrm{~ms}\) to minimum (non-zero) value where it meets the printed line after 4.0 ms B1 correct concave curvature, with gradient never positive B1 minimum potential difference 6.0 V B1
Question 5(b)(ii)
5(b)(ii)
Determine the time, in s , for which the capacitor is discharging between times \(t=1.0 \mathrm{~ms}\) and \(t=5.0 \mathrm{~ms}\). time = s
Mediumstructured1 marks
Answer
time \(=3.5 \times 10^{-3} \mathrm{~s}\) A1
Question 5(b)(iii)
5(b)(iii)
Use your answers in (b)(i) and (b)(ii) to calculate the resistance R. R= \(\Omega[2]\)
Hardstructured2 marks
Answer
\[ \begin{aligned} V=V_{0} \exp (-t / R C) 6.0=8.0 \exp \left[\left(-3.5 \times 10^{-3}\right) /\left(85 \times 10^{-6} \times R\right)\right] \end{aligned} \] C1 \(R=140 \Omega\) A1
Question 5
5
Fig. 5.1 shows four diodes and a load resistor of resistance \(1.2 \mathrm{k} \Omega\), connected in a circuit that is used to produce rectification of an alternating voltage.
structured9 marks
Question 5(a)
5(a)
2 marks
Question 5(a)(i)
5(a)(i)
State what is meant by rectification.
Easystructured1 marks
Answer
conversion (from a.c.) to d.c. B1
Question 5(a)(ii)
5(a)(ii)
State the type of rectification produced by the circuit in Fig. 5.1.
Easystructured1 marks
Answer
full-wave (rectification) B1
Question 5(b)
5(b)
A sinusoidal alternating voltage \(V_{\text {IN }}\) is applied across the input terminals X and Y. The variation with time t of \(V_{\text {IN }}\) is given by the equation where \(V_{\text {IN }}\) is in volts and t is in seconds.
structured1 marks
Question 5(b)(i)
5(b)(i)
On Fig. 5.1, label the output terminals P and Q with the appropriate symbols to indicate the polarity of the output voltage \(V_{\text {OUT }}\).
Mediumstructured1 marks
Answer
P labelled - and Q labelled + B1
Question 5(c)
5(c)
The output voltage in (b) is smoothed by adding a capacitor to the circuit in Fig. 5.1. The difference between the maximum and minimum values of the smoothed output voltage is 10 % of the peak voltage.
structured6 marks
Question 5(c)(i)
5(c)(i)
On Fig. 5.1, draw the circuit symbol for a capacitor showing the capacitor correctly connected into the circuit.
Easystructured1 marks
Answer
correct symbol used for capacitor and capacitor connected in parallel with the \(1.2 \mathrm{k} \Omega\) resistor. B1
Question 5(c)(ii)
5(c)(ii)
On Fig. 5.2, sketch the variation with t of the smoothed output voltage.
Mediumstructured2 marks
Answer
straight lines or curves, with negative decreasing gradients, drawn between adjacent peaks, from top of first peak to meet line going up to next peak B1 lines, from one peak to the line going up to the next peak, show a drop in p.d. of \(1 \frac{1}{2}\) small squares B1
Question 5(c)(iii)
5(c)(iii)
Calculate the capacitance C of the capacitor.
Hardstructured3 marks
Answer
\[ V=0.90 \times 6.0(=5.4 \mathrm{~V}) \] or discharge time (for each cycle) \(=0.034 \mathrm{~s}\) C1 \[ V=V_{0} \exp (-t / R C) \] \(5.4=6.0 \exp \left[-0.034 /\left(1.2 \times 10^{3} \times C\right)\right]\) C1 \(C=2.7 \times 10^{-4} \mathrm{~F}\) A1
Question 5
5
An analogue signal is to be transmitted to a receiver. Before transmission, the signal passes through an analogue-to-digital converter (ADC). After transmission it passes through a digital-to-analogue converter (DAC) before finally reaching the receiver, as shown in Fig. 5.1.
structured8 marks
Question 5(a)
5(a)
State two advantages of converting the signal into digital form for transmission. 1. 2.
Mediumstructured2 marks
Answer
noise can be removed/signal can be regenerated - extra bits can be added for error-checking - signal can be encrypted (for increased security) - data compression/multiplexing is possible Any two points, 1 mark each B2
Question 5(b)
5(b)
The variation with time of the potential difference (p.d.) of the input signal is shown in Fig. 5.2. The ADC has a sampling frequency of 250 Hz and uses 4-bit sampling, with the least significant bit corresponding to 1 mV . The signal is first sampled at time 0 , when the sampled bits are 0001.
structured3 marks
Question 5(b)(i)
5(b)(i)
State the sampled bits at time 4 ms and time 8 ms . 4 ms : 8 ms :
Mediumstructured1 marks
Answer
\(4 \mathrm{~ms}: 0101\) and \(8 \mathrm{~ms}: 0100\) B1
Question 5(b)(ii)
5(b)(ii)
Part of the signal received by the receiver, after the sampled signal has passed through the DAC, is shown in Fig. 5.3. On Fig. 5.3, complete the line to show the received signal for time 0 to time 12 ms .
Mediumstructured2 marks
Answer
sketch: horizontal line continues to 8 ms , then new horizontal line from 8 ms to 12 ms B1 level of line after 8 ms is 4 mV B1
Question 5(c)
5(c)
The ADC in (b) is replaced with one that has a sampling frequency of 500 Hz and uses 3-bit sampling, with the least significant bit corresponding to 2 mV . On Fig. 5.4, sketch the signal that is now received, after passing through the DAC, from time 0 to time 12 ms .
Hardstructured3 marks
Answer
sketch: series of steps of width 2 ms B1 step heights at 0,2,4,6,4,6 mV 2 marks if all correct, 1 mark if only one incorrect B2
Question 6
6
A bridge rectifier consists of four ideal diodes A, B, C and D, connected as shown in Fig. 6.1. Fig. 6.1 An alternating supply is applied between the terminals X and Y.
structured5 marks
Question 6(a)
6(a)
2 marks
Question 6(a)(i)
6(a)(i)
On Fig. 6.1, label the positive (+) connection to the load resistor R.
Easystructured1 marks
Answer
connection to 'top' of resistor labelled as positive
Question 6(a)(ii)
6(a)(ii)
State which diodes are conducting when terminal Y of the supply is positive. diode and diode
Easystructured1 marks
Answer
diode B and diode D
Question 6(b)
6(b)
The variation with time t of the potential difference V across the load resistor R is shown in Fig. 6.2. The load resistor R has resistance \(2700 \Omega\).
structured1 marks
Question 6(b)(ii)
6(b)(ii)
On Fig. 6.1, draw the symbol for a capacitor, connected so as to increase the mean power dissipated in the resistor R.
Easystructured1 marks
Answer
capacitor, correct symbol, connected in parallel with R
Question 6(c)
6(c)
The capacitor in (b)(ii) is now removed from the circuit. The diode A in Fig. 6.1 stops functioning, so that it now has infinite resistance. On Fig. 6.2, draw the variation with time t of the new potential difference across the resistor R.
Mediumstructured2 marks
Answer
graph: half-wave rectification same period and same peak value
Question 5
5
The components for a bridge rectifier are shown in Fig. 5.1.
structured6 marks
Question 5(a)
5(a)
Complete the circuit of Fig. 5.1 by showing the connections of the supply and of the load to the diodes.
Mediumstructured2 marks
Question 5(b)
5(b)
Suggest one advantage of the use of a bridge rectifier, rather than a single diode, for the rectification of alternating current.
Mediumstructured1 marks
Question 5(c)
5(c)
State
structured3 marks
Question 5(c)(i)
5(c)(i)
what is meant by smoothing,
Easystructured1 marks
Question 5(c)(ii)
5(c)(ii)
the effect of the value of the capacitance of the smoothing capacitor in relation to smoothing.
Mediumstructured2 marks
Question 5
5
Part of an electric circuit is shown in Fig. 5.1. The circuit is used to produce half-wave rectification of an alternating voltage of potential difference (p.d.) \(V_{\text {IN }}\). The output p.d. across the \(14 \mathrm{k} \Omega\) resistor is \(V_{\text {OUT }}\).
structured4 marks
Question 5(a)
5(a)
2 marks
Question 5(a)(i)
5(a)(i)
A component is missing from the circuit of Fig. 5.1. Complete the circuit diagram in Fig. 5.1 by adding the circuit symbol for the missing component, correctly connected.
Easystructured1 marks
Answer
correct circuit symbol for a diode shown correctly connected in series with the wires leading into and out of the dotted box B1
Question 5(a)(ii)
5(a)(ii)
A capacitor C is shown in the circuit of Fig. 5.1. State the effect on \(V_{\text {OUT }}\) of including the capacitor in the circuit.
Mediumstructured1 marks
Answer
smoothing / \(V_{\text {out }}\) is smoothed B1
Question 5(c)
5(c)
The circuit of Fig. 5.1 is modified so that it produces full-wave rectification of an input voltage. Suggest, with a reason, how \(V_{\text {OUT }}\) now varies with time when \(V_{\text {IN }}\) is as shown in Fig. 5.2.
Mediumstructured2 marks
Answer
\(V_{\text {IN }}\) has constant magnitude in both positive and negative directions B1 (so) \(V_{\text {out }}\) is (now) constant / \(V_{\text {out }}\) does not vary with time B1
Question 6
6
A student is asked to design a circuit by which a direct voltage of peak value 9.0 V is obtained from a 240 V alternating supply. The student uses a transformer that may be considered to be ideal and a bridge rectifier incorporating four ideal diodes. The partially completed circuit diagram is shown in Fig. 6.1.
structured5 marks
Question 6(a)
6(a)
On Fig. 6.1, draw symbols for the four diodes so as to produce the polarity across the load as shown on the diagram.
Easystructured2 marks
Answer
all four diodes correct to give output, regardless of polarity connected for correct polarity
Question 6(b)
6(b)
Calculate the ratio ratio =
Mediumstructured3 marks
Answer
\(N_{S} / N_{P}=V_{S} / V_{P}\) \(V_{0}=\sqrt{ } 2 \times V_{\mathrm{rms}}\) ratio \(=9.0 /(\sqrt{ } 2 \times 240)\)