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Question
A coil of resistance 10 Ω and inductance 100mH and a capacitor of variable capacitance are connected across a 20V, 50Hz A.C. supply. At what capacitance will resonance occur?
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Solution
Given:
R = 10 Ω, L = 100 mH = 100 × 10-3 H = 10-1 H
V = 20 volt, fr = 50 Hz
To find: Capacitance (C)
Formula: fr = `1/(2pi sqrt"LC")`
Calculation:
From formula,
C = `1/(4pi^2"f"_"r"^2"L")`
= `1/(4 xx (3.142)^2 xx 50^2 xx 10^-1)`
= 101.3 × 10-6 F
= 101.3 μF
The resonance will occur when capacitance will have a value of 101.3 μF.
Notes
[Note - Answer calculated above is in accordance with the textual method of calculation.]
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