CBSE 2025, Set 2

Question

An ac source is connected to a resistor and an inductor in series. The voltage across the resistor and inductor are $8	ext{ V}$ and $6	ext{ V}$ respectively. The voltage of the source is: A). $10	ext{ V}$ B). $12	ext{ V}$ C). $14	ext{ V}$ D). $16	ext{ V}$

Edvaya · Accepted Answer

The correct answer is $10	ext{ V}$. In a series LR circuit, the voltage across the resistor ($V_R$) and the voltage across the inductor ($V_L$) are not in phase. $V_L$ leads $V_R$ by a phase angle of $90^\circ$ ($\frac{\pi}{2}$ rad).

Therefore, they cannot be added algebraically. The total voltage of the source ($V$) is the phasor sum of $V_R$ and $V_L$:

$$V = \sqrt{V_R^2 + V_L^2}$$

Given $V_R = 8	ext{ V}$ and $V_L = 6	ext{ V}$:
$$V = \sqrt{8^2 + 6^2}$$
$$V = \sqrt{64 + 36}$$
$$V = \sqrt{100} = \boxed{10	ext{ V}}$$

> In AC circuits, instantaneous voltages add algebraically, but rms/peak voltages add as phasors.

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Physics > Magnetism Induction And Alternating Current > Alternating Current

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