7.18 A circuit containing a 80 mH inductor and a 60 $μ$ F 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'.]

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Payal Gupta | Contributor-Level 10

8 months ago

7.18 Inductance, L = 80 mH = 80 $* 10^{- 3}$ H

Capacitance, C = 60 $μ F$ = 60 $* 10^{- 6}$ F

Supply voltage, V = 230 V

Supply frequency, $ν$ = 50 Hz

Peak voltage, $V_{0}$ = V $\sqrt 2$ = 325.27 V

Angular frequency, $ω$ = 2 $π ν$ = 2 $π * ν$ = 2 $π * 50$ = 100 $π$ rad/s

Maximum current is given as:

$I_{0}$ = $\frac{V_{0}}{(ω L - \frac{1}{ω C})}$ = $\frac{325.27}{(100 π * 80 * 10^{- 3} - \frac{1}{100 π * 60 * 10^{- 6}})}$ = $-$ 11.65 A

The negative sign is due to $ω L$ $< \frac{1}{ω C}$

Amplitude of maximum current $|I_{0}|$ = 11.6

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Physics Ncert Solutions Class 12th 2023

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