4 questions
In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance \( C \, \mu \text{F} \) across a \( 200 \, \text{V} \), \( 50 \, \text{Hz} \) supply. The power consumed by the lamp is \( 500 \, \text{W} \) while the voltage drop across it is \( 100 \, \text{V} \). Assume that there is no inductive load in the circuit. Take rms values of the voltages. The magnitude of the phase angle (in degrees) between the current and the supply voltage is \( \phi \). Assume, \( \pi\sqrt{3} \approx 5 \).
The value of \( \phi \) is ________.
A series LCR circuit is connected to a \( 45\sin(\omega t) \) Volt source. The resonant angular frequency of the circuit is \( 10^{5} \, \text{rad} \, \text{s}^{-1} \) and current amplitude at resonance is \( I_{0} \). When the angular frequency of the source is \( \omega = 8 \times 10^{4} \, \text{rad} \, \text{s}^{-1} \), the current amplitude in the circuit is \( 0.05 I_{0} \). If \( L = 50 \, \text{mH} \), match each entry in List-I with an appropriate value of from List-II and choose the correct option.
A circuit with an electrical load having impedance \( Z \) is connected with an AC source as shown in the diagram. The source voltage varies in time as \( V(t) = 300 \sin(400 t) \, \text{V} \), where \( t \) is time in \( \text{s} \). List-I shows various options for the load. The possible currents \( i(t) \) in the circuit as a function of time are given in List-II.
Choose the option that describes the correct match between the entries in List-I to those in List-II.
In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance \( C \, \mu \text{F} \) across a \( 200 \, \text{V} \), \( 50 \, \text{Hz} \) supply. The power consumed by the lamp is \( 500 \, \text{W} \) while the voltage drop across it is \( 100 \, \text{V} \). Assume that there is no inductive load in the circuit. Take rms values of the voltages. The magnitude of the phase angle (in degrees) between the current and the supply voltage is \( \phi \). Assume, \( \pi\sqrt{3} \approx 5 \).
The value of \( C \) is ________.
