In a black box of unknown elements ( L or R or any other combination), an ac voltage E=E0 sin (ω t+φ) is applied and current in the circuit was found to be I=I0 sin [ω t+φ+(π / 4)]. Then the unknown elements in the box may be

Question

(A) only capacitor (B) inductor and resistor both (C) either capacitor, resistor, and inductor or only capacitor and resistor (D) only resistor

Tardigrade Admin · Accepted Answer

Since current is leading emf, capacitor must be present in the circuit. Along with capacitor, there can be either (i) only resistor or (ii) resistor and inductor if

X_{C} > X_{L}

.
In both of the above conditions, we can obtain a phase difference of

π /4

with current leading emf.

Q. In a black box of unknown elements ( L or R or any other combination), an ac voltage E=E0​sin(ωt+ϕ) is applied and current in the circuit was found to be I=I0​sin[ωt+ϕ+(π/4)]. Then the unknown elements in the box may be

only capacitor

inductor and resistor both

either capacitor, resistor, and inductor or only capacitor and resistor

only resistor

Since current is leading emf, capacitor must be present in the circuit. Along with capacitor, there can be either (i) only resistor or (ii) resistor and inductor if XC​>XL​. In both of the above conditions, we can obtain a phase difference of π/4 with current leading emf.

Q. In a black box of unknown elements ( $L$ or $R$ or any other combination), an ac voltage $E = E_{0} sin (ω t + ϕ)$ is applied and current in the circuit was found to be $I = I_{0} sin [ω t + ϕ + (π /4)]$ . Then the unknown elements in the box may be

Since current is leading emf, capacitor must be present in the circuit. Along with capacitor, there can be either (i) only resistor or (ii) resistor and inductor if $X_{C} > X_{L}$ .
In both of the above conditions, we can obtain a phase difference of $π /4$ with current leading emf.