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Question
Figure 4 below shows a capacitor C, an inductor L and a resistor R, connected in series
to an a.c. supply of 220 V
Calculate:
1) The resonant frequency of the given CLR circuit.
2) Current flowing through·the circuit.
3) Average power consumed by the circuit.
Solution
`E_"rms" = 220 V`
`C = 25 muF`
`L = (4/pi^2)H`
R = 100 Ω
1) Resonant Frequency
`f_r = 1/(2pisqrt(LC))`
`= 1/(2xx 3.14 xx sqrt(4/pi^2 xx 25 xx 10^(-6)))`
`= 1/(2xx3.14 xx 2/3.14 xx 5 xx 10^(-3)) `
= 50 Hz
2) Inpedance (Z) = `sqrt(R^2 + (X_L - X_C)^2)`
`X_L = 127.3 Ω, X_C = 127.3 Ω`
Z = `sqrt(100^2 + (127.3 - 127.3)^2 )`
`Z = sqrt(100^2)`
Z = 100 Ω
`I_"rms" = E_"rms"/2`
`= 220/100`
`I_"rms" = 2.2 A`
3) Average power consumed by the circuit
Power = `E_"rms" xx I_"rms" xx R/sqrt(R^2 + (Lomega - 1/(Comega)))`
z = R
∴ Power = `E_"rms" xx I_"rms"`
Power = 484 watt
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