Download 1E6_Tutorial 8

Tutorial No. 8
Problem 1
A circuit having a resistance of 4 , an inductance of 0.5 H and a variable capacitor in
series, is connected across a 100 V, 50 Hz supply. Calculate
(i)
the capacitance to give resonance;
(ii)
the voltages across the inductance and the capacitance, and
(iii)
the Q factor of the circuit.
Problem 2
Explain the meaning of the term resonance as applied to a series a.c. circuit. Draw the
phasor diagram to illustrate this condition
A series circuit consists of 0.5 F capacitor, a coil of inductance 0.32 H and a resistance
of 40 , and a 20  non-inductive resistor. Calculate the value of the resonant frequency
of the circuit.
When the circuit is connected to a 30 V a.c. supply at this resonant frequency, determine:
(a) the potential difference across each of the three components;
(b) the current flowing in the circuit.
Problem 3.
A constant voltage at a frequency of 1 MHz is maintained across a circuit consisting of an
inductor in series with a variable capacitor. When the capacitor is reduced from 300 pF
to 284 pF, the current is 0.707 of its maximum value. Find
(i)
the inductance and the resistance of the inductor, and
(ii)
the Q factor of the inductor at 1 MHz. Sketch the phasor diagram for each
condition
Problem 4
Express in rectangular and polar notations, the impedance of each of the following
circuits at a frequency of 50 Hz
(i)
a resistance of 20  in series with an inductance of 0.1 H
(ii)
a resistance of 50  in series with a capacitance of 40 F, and
(iii)
the circuits of (i) and (ii) in series.
If the terminal voltage is 230 V, 50 Hz, calculate the value of the current in each case and
the phase of each current relative to the applied voltage.