Question

The variation between V and I with time (t) in two alternative circuits is shown in the above graphs. Which one of the curves of circuit is capacitive and which one is resistive?

Hint:

In a resistor V and I are in phase; in a capacitor the current leads the voltage by \( 90^{\circ} \). Look for which graph shows I peaking before V.

Answer 1

Step 1 (Phase rule for a resistor): In a purely resistive AC circuit the current follows the voltage exactly. Both \( V \) and \( I \) reach their peaks and zeros at the same instant, so the phase difference between them is zero (they are in phase).
Step 2 (Phase rule for a capacitor): In a purely capacitive AC circuit the current leads the voltage by a quarter cycle, i.e. by \( 90^{\circ} \). The \( I \) curve therefore reaches its peak before the \( V \) curve.
Step 3 (Read the two graphs): In the left graph the \( V \) and \( I \) curves rise, peak and fall together with no time gap, showing they are in phase.
In the right graph the \( I \) curve reaches its maximum a quarter cycle earlier than the \( V \) curve, showing that current leads voltage.
Step 4 (Conclusion):
\[\boxed{\text{Left graph} \rightarrow \text{Resistive},\qquad \text{Right graph} \rightarrow \text{Capacitive}}\]