Question

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. 

Answer 1

Given:

f = 60 Hz, e_rms = 110 V, L = 0.8 H,
R = 50 Ω, C = 8 μF
V = 20 volt  

To find: Current in the circuit (i_rms)

Formulae: 

1. X_L = 2πfL
2. X_c = `1/(2pi"fC")`
3. Z = `sqrt("R"^2 + ("X"_"L" - "X"_"C")^2)`
4. `"i"_"rms" = "e"_"rms"/"Z"`

Calculation:

From formula (i),

X_L = 2 × 3.142 × 60 × 0.8 = 301.63 Ω

From formula (ii),

X_C = `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),

i_rms = `110/58.26` = 1.88 A

The current in the circuit is 1.88 A.