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14 Electromagnetism II
14.10 A simple alternator, when rotating at 50 revolutions/s, gives a 50 Hz alternating voltage of rms value 24 V. A 4.0 resistance R and a 0.01 H inductance
L are connected in series across its terminals. Assuming that the internal
impedance of the generator can be neglected, find (a) the rms current flowing;
(b) the power converted into heat; (c) the rms potential difference across each
component.
14.11 An AC circuit consists of only a resistor R = 100 and a source voltage
V = 0.5 V m at time t = 1/360 s. Assuming that at t = 0, V = 0, find the
frequency.
14.12 Given that for a series LCR circuit the equation is
d 2 V
dt 2 +
R
L
dV
dt
+
1
LC
V = 0
If a similar equation is to be used for a parallel LCR circuit as in Fig. 14.1,
then show that
R p =
L
C R
Fig. 14.1
14.13 Verify the equation c =
1
√ μ 0 ε 0
.
14.14 Show that in the usual notation the following combinations of physical quantities have the units of time: (a) RC, (b) L/R, (c)
√
LC.
14.15 In an oscillating RLC circuit the amplitude of the charge oscillations drops
to one-half its initial value in 4 cycles. Show that the fractional decrement of
the resonance frequency is approximately given by
ω
ω = 0.00038.
14.16 Derive the equation for the current in a damped LC circuit for low damping.