(i) The value of current amplitude is

Question

Read the following paragraph and answer the questions that follow. 

Power Associated with Inductor and Capacitor

The power averaged over one full cycle of a.c. is known as average power. It is also known as true power.

\(P_{av}=V_{rms}I_{rms}\,cos\phi = \frac {V_0 I_ 0}{2}cos \phi .\)

Root mean square or simply rms watts refer to continuous power. 

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.

(i) The value of current amplitude is 

(a) 15 A 

(b) 11.63 A 

(c) 17.65 A 

(d) 6.33 A 

(ii) Find rms value. 

(a) 6 A 

(b) 5.25 A 

(c) 8.23 A 

(d) 7.52 A 

(iii) The average power transferred to inductor is 

(a) zero 

(b) 7 W 

(c) 2.5 W 

(d) 5 W 

(iv) The average power transferred to the capacitor is 

(a) 5 W 

(b) zero 

(c) 11 W 

(d) 15 W

OR 

What is the total average power absorbed by the circuit? 

(a) zero 

(b) 10 W 

(c) 2.5 W 

(d) 15 W

Answer 1

(i) (b) 11.63 A 

Inductance, L = 80 mH = 80 × 10^-3 H

Capacitance, C = 60 μF = 60 × 10^-6 F, V = 230 V

Frequency, \(\upsilon\) = 50 Hz

Amplitude of maximum current, I₀ = 11.63 A

(ii) (c) 8.23 A 

rms value of current,

Negative sign appears as ωL < 1/ωC.

(iii) (a) zero 

Average power consumed by the inductor is zero because of phase difference of π/2 between voltage and current through inductor.

(iv) (b) zero 

Average power consumed by the capacitor is zero because of phase difference of π/2 between voltage and current through capacitor.

OR

(a) zero 

Total average power absorbed by circuit is zero.