In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance C μ F across a 200 V , 50 Hz supply. The power consumed by the lamp is 500 W while the voltage drop across it

Question

In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance $C μ F$ across a $200 V, 50 Hz$ supply. The power consumed by the lamp is $500 W$ while the voltage drop across it is $100 V$ . Assume that there is no inductive load in the circuit. Take $r m s$ values of the voltages. The magnitude of the phaseangle (in degrees) between the current and the supply voltage is $φ$ . Assume, $π 3 \approx 5$ .
The value of $ϕ$ is _____.

TestHub · Accepted Answer

Given, P = 500 W V R = 100 V f = 50 Hz V r m s = 200 V P = V R 2 R ⇒ R = V R 2 P ⇒ R = 100 2 500 ∴ R = 20 Ω Now current in the circuit, i = i r m s = voltage across resistor resistance i = 100 20 i = 5 A Phasor diagram of the given circuit for voltage, Now, V 2 = V C 2 + V R 2 ⇒ 200 2 = V C 2 + 100 2 ⇒ V C = 100 3 V Now, V C = 100 3 V = I X C ⇒ X C = 100 3 5 = 20 3 Ω and X C = 1 2 π f C ⇒ 20 3 = 1 2 π × 100 C ⇒ C = 100 μF From the phasor diagram, tan ϕ = X C R = 20 3 20 = 3 ⇒ ϕ = 60 °

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