Correct sequence for instantaneous current and voltage equations for the circuit with R only, L only, C only and series LCR will be respectively (where Ø is determined by circuit parameters):
A. ε = ε0 sin ωt , i = i0 sin (ωt – π/2)
B. ε = ε0 sin(ωt) , i = i0 sin(ωt ± Ø)
C. ε = ε0 sin ωt , i = i0 sin ωt
D. ε = ε0 sin(ωt) , i = i0 sin (ωt + π/2)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → C, A, D, B
With \( \varepsilon = \varepsilon_0 \sin \omega t \) applied, the phase of the current relative to the voltage identifies each circuit.
R only: the current is in phase with the voltage, \( i = i_0 \sin \omega t \). This is (C).
L only: the current lags the voltage by \( \pi/2 \), \( i = i_0 \sin(\omega t - \pi/2) \). This is (A).
C only: the current leads the voltage by \( \pi/2 \), \( i = i_0 \sin(\omega t + \pi/2) \). This is (D).
Series LCR: the current leads or lags by an angle \( \phi \) with \( \tan\phi = (X_C - X_L)/R \), depending on which reactance is larger. This is (B).
So the sequence is C, A, D, B.
NCERT (2026-27):
Summary – “… 1. An alternating voltage \( v = v_m \sin\omega t \) applied to a resistor R drives a current \( i = i_m \sin\omega t \) in the resistor, \( i_m = \frac{v_m}{R} \). The current is in phase with the applied voltage.”
Summary – “… 3. An ac voltage \( v = v_m \sin\omega t \) applied to a pure inductor L, drives a current in the inductor \( i = i_m \sin(\omega t - \pi/2) \), where \( i_m = v_m/X_L \). … The current in the inductor lags the voltage by π/2.”
Summary – “… 4. An ac voltage \( v = v_m \sin\omega t \) applied to a capacitor drives a current in the capacitor: \( i = i_m \sin(\omega t + \pi/2) \). … The current through the capacitor is π/2 ahead of the applied voltage.”
Summary – “… 5. For a series RLC circuit driven by voltage \( v = v_m \sin\omega t \), the current is given by
\( \displaystyle i = i_m \sin(\omega t + \phi) \)”