NEET-XII-Physics
07: Alternating Current
- #18A 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’.]Ans : Inductance, L = 80 mH = 80 × 10-3 H
Capacitance, C = 60 μF = 60 × 10-6 F
Supply voltage, V = 230 V
Frequency, ν = 50 Hz
Angular frequency, ω = 2``\pi``ν= 100 ``\pi`` rad/s
Peak voltage, V0 =
(a) Maximum current is given as:
The negative sign appears because
Amplitude of maximum current,
Hence, rms value of current,
(b) Potential difference across the inductor,
VL= I × ωL
= 8.22 × 100 ``\pi`` × 80 × 10-3
= 206.61 V
Potential difference across the capacitor,
(c) Average power consumed by the inductor is zero as actual voltage leads the current by
.
(d) Average power consumed by the capacitor is zero as voltage lags current by.
(e) The total power absorbed (averaged over one cycle) is zero.
- #18-aObtain the current amplitude and rms values.Ans : Maximum current is given as:
The negative sign appears because
Amplitude of maximum current,
Hence, rms value of current,
- #18-bObtain the rms values of potential drops across each element.Ans : Potential difference across the inductor,
VL= I × ωL
= 8.22 × 100 ``\pi`` × 80 × 10-3
= 206.61 V
Potential difference across the capacitor,
- #18-cWhat is the average power transferred to the inductor?Ans : Average power consumed by the inductor is zero as actual voltage leads the current by.
- #18-dWhat is the average power transferred to the capacitor?Ans : Average power consumed by the capacitor is zero as voltage lags current by.
- #18-eWhat is the total average power absorbed by the circuit? [‘Average’ implies ‘averaged over one cycle’.]Ans : The total power absorbed (averaged over one cycle) is zero.