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प्रश्न
Find the current in a circuit consisting of a coil and a capacitor in series with an A.C source of 110V (r.m.s.), 60Hz. The inductance of a coil is 0.80 H and its resistance is 50Ω. The capacitance of a capacitor is 8µF.
उत्तर
Given:
f = 60 Hz, erms = 110 V, L = 0.8 H,
R = 50 Ω, C = 8 μF
V = 20 volt
To find: Current in the circuit (irms)
Formulae:
- XL = 2πfL
- Xc = `1/(2pi"fC")`
- Z = `sqrt("R"^2 + ("X"_"L" - "X"_"C")^2)`
- `"i"_"rms" = "e"_"rms"/"Z"`
Calculation:
From formula (i),
XL = 2 × 3.142 × 60 × 0.8 = 301.63 Ω
From formula (ii),
XC = `1/(2 xx 3.142 xx 60 xx 0.8 xx 10^-6)` = 331.53 Ω
From formula (iii),
Z = `sqrt(50^2 + (301.63 - 331.53)^2)` = 58.26 Ω
From formula (iv),
irms = `110/58.26` = 1.88 A
The current in the circuit is 1.88 A.
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