Question

In an AC circuit the voltage applied is $v = 230\sin(\omega t - 30^\circ)$ volts. If the current flowing is $i = 47\sin(\omega t + 10^\circ)$ amps, then the current _______.

• A. lags the voltage by $40^\circ$
• B. lags the voltage by $20^\circ$
• C. leads the voltage by $20^\circ$
• D. leads the voltage by $40^\circ$

Hint:

Always subtract voltage phase from current phase: $\phi_I - \phi_V$. Positive result = leading, negative = lagging.

Answer 1

The Correct Option is D

Step 1: Write the phase angles.
Voltage: $\phi_V = -30^\circ$
Current: $\phi_I = +10^\circ$ 
Step 2: Calculate phase difference.
\[ \Delta \phi = \phi_I - \phi_V = 10 - (-30) = 40^\circ \] Step 3: Interpret the result.
Positive phase difference means current is ahead of voltage.
Conclusion: Current leads the voltage by $\boxed{40^\circ}$.