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NCERT Class XII Chapter
Alternating Current
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Question : 18 of 26
Marks: +1, -0
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’.]
Solution:  
(a) Inductive reactance, XLX_L = 2πfL
XLX_L = 2π(50) 80 × 10310^{-3} = 25.12 Ω
Capacitive reactance, XCX_C = 12πfC\frac{1}{2\pi fC}
XCX_C = 12×3.14×50×60×106\frac{1}{2 \times 3.14 \times 50 \times 60 \times 10^{-6}} = 53.05 Ω
Impedance = XCXLX_C - X_L = 53.05 – 25.12 = 27.93 Ω
rms value of current, IvI_v = EvZ\frac{E_v}{Z} = 23027.93\frac{230}{27.93} = 8.235 A
Peak value I0I_0 = Iv2I_v \sqrt{2} = 11.644 A
(b) Potential drop across L, VLV_L = IvXLI_v X_L = 206.68 V
Potential drop across C, VCV_C = IvXCI_v X_C = 436.87 V
(c) Average power transferred to inductor is zero, because of phase difference π/2.
P = EvIvE_v I_v cos ϕ
ϕ = π/2, ∴ P = 0
(d) Average power transferred to capacitor is also zero, because of phase difference π/2.
P = EvIvE_v I_v cos ϕ
ϕ = π/2, ∴ P = 0
(c) Total power absorbed by the circuit
PTotalP_{\text{Total}} = PL+PCP_L + P_C = 0
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