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.

Question 1

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 sin ωt.

(a) Determine the value of

(i) V0, [1]

(ii) ω. [1]

(b) 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. [3]

Reference: Past Exam Paper – November 2015 paper 43 Q7

Solution:

(a)

(i)

{V_rms = V₀ / √2

V₀ = V_rms × √2}

V0 (= 14 √2 ) = 19.8 (20) V

(ii)

{ω = 2πf}

ω (= 2π × 750) = 4700 rad s^–1

(b)

{Capacitance C = Q / V

Since the capacitance is large, the amount of charge Q required will also be large.}

A large amount of charge is required to charge the capacitor {of large capacitance}.

{The output of the supply is sinusoidal, so the capacitor would charge and discharge very rapidly (depending on the frequency). The high frequency gives rise to a very short charging/discharging time.}

The capacitor would charge and discharge rapidly.

{I = Q / t,} As current is the charge per unit time, the large charge would produce a large current.