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’.]

The output of a step-down transformer is measured to be 24 V when connected to a 12-watt light bulb. The value of the peak current is ______.

In the Figure below, the current-voltage graphs for a conductor are given at two different temperatures, T₁ and T_2.

1. At which temperature T₁ or T₂ is the resistance higher?
2. Which temperature (T₁ or T₂) is higher?

A coil of inductance 5.0 mH and negligible resistance is connected to the oscillator of the previous problem. Find the peak currents in the circuit for ω = 100 s⁻¹, 500 s⁻¹, 1000 s⁻¹.

A device X is connected across an ac source of voltage V = V₀ sin ωt. The current through X is given as 

`I = I_0 sin (omega t + pi/2 )`

1) Identify the device X and write the expression for its reactance.

2) Draw graphs showing the variation of voltage and current with time over one cycle of ac, for X.

3) How does the reactance of the device X vary with the frequency of the ac? Show this variation graphically.

4) Draw the phasor diagram for the device X.

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.

Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.