Chapter 21. Alternating Currents

Question 1

What is the equation for instantaneous current and voltage of an alternating current?

Answer 1

I = I₀sin(ωt) and V = V₀sin(ωt)

Question 2

What is meant by the peak-to-peak voltage

Answer 2

2V₀

Question 3

Describe how you would obtain frequency of an alternating current?

Answer 3

You can use a cathode ray oscilloscope and use the time base to find the period then invert the period.

Question 4

What is the equation for the instantaneous power of an alternating current?

Answer 4

P = VI = I²R but I = I₀sin(ωt) so P = I₀²sin²(ωt)

Question 5

What is the formula for average power supplied to a resistor by an alternating current?

Answer 5

since P = I₀²sin²(ωt) and I₀^{2</sub> and R are constant, so the average power of P depends on the average value of sin(ωt) which is half, so <P> = (1/2)I₀2R = (1/2)V₀2/R, N.B for a sinusodial alternating current, the average power is half the maximum power.}

Question 6

Derive the root-mean-square voltage and current of an alternating current

Answer 6

Taking the average of instantaneous current will give <I²> = (1/2)I₀⁰ so I_rms = I₀/√2 same goes for voltage. The r.m.s value is the direct current or voltage that would produce thermal energy at the same rate in a resistor.

Question 7

Describe half-wave rectification

Answer 7

One diode in the circuit producing positive half-cycles of the input voltage.

Question 8

Describe full-wave rectification

Answer 8

Four diodes in the circuit converting all negative cycles to positive, N.B the circuit is known as a bridge rectifier

Question 9

What is smoothing and how is it achieved?

Answer 9

The reductions in fluctuations of the input a.c voltage by use of capacitors. Knowing the graph would prove to be very useful, a larger value of RC will reduce the ripple.

Question 10

Explain the principle of the transformer

Answer 10

An input alternative e.m.f sends an a.c which creates an alternating flux in the core. This induces an alternating e.m.f at the other end. Vs/Vp = Ns/Np and Pi = Po

Question 11

What causes energy losses in a transformer?

Answer 11

1. Flux leakage 2.Induced eddy currents 3. Hysteresis loses - core becomes hot due to alternating magnetic fields, 4. Resistance of the wire

Question 12

Why a.c and not d.c for power transmission?

Answer 12

High voltage transmissions reduces power losses, turning of a switch under d.c will cause a spark, alternators produce higher p.ds