In the 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 phase-angle (in degrees) between the current and supply voltage is φ . Assume, π √3 ≈ 5. The value of φ is .

Question

In the 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 phase-angle (in degrees) between the current and supply voltage is φ . Assume, π √3 ≈ 5. The value of φ is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

cos φ=( R / Z )=(20/40)=(1/2) ⇒ φ=60°

cosϕ=ZR​=4020​=21​ ⇒ϕ=60∘

$cos ϕ = \frac{R}{Z} = \frac{20}{40} = \frac{1}{2}$
$\Rightarrow ϕ = 6 0^{\circ}$