Peak and Rms Value of Alternating Current Or Voltage

A circuit containing a 80 mH inductor and a 60 µF capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible.

(a) Obtain the current amplitude and rms values.

(b) Obtain the rms values of potential drops across each element.

(c) What is the average power transferred to the inductor?

(d) What is the average power transferred to the capacitor?

(e) What is the total average power absorbed by the circuit?
[‘Average’ implies ‘averaged over one cycle’.]

A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is 0.5 Ω per km. The town gets power from the line through a 4000-220 V step-down transformer at a sub-station in the town.

(a) Estimate the line power loss in the form of heat.

(b) How much power must the plant supply, assuming there is negligible power loss due to leakage?

(c) Characterise the step up transformer at the plant.

Do the same with the replacement of the earlier transformer by a 40,000-220 V step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred?

A resistor of resistance 100 Ω is connected to an AC source ε = (12 V) sin (250 π s⁻¹)t. Find the energy dissipated as heat during t = 0 to t = 1.0 ms.

In a series RC circuit with an AC source, R = 300 Ω, C = 25 μF, ε₀ = 50 V and ν = 50/π Hz. Find the peak current and the average power dissipated in the circuit.

An alternating current is given by i = i₁ cos ωt + i₂ sin ωt. The rms current is given by

An alternating current of peak value 14 A is used to heat a metal wire. To produce the same heating effect, a constant current i can be used, where i is