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.

Answer 1

`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