Electromagnetic Induction and Alternating Current 6 Question 8
####8. You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an $\mathrm{AC}$ voltage source of $50 \mathrm{~Hz}$ frequency (the next three circuits) in different ways as shown in Column II. When a current $I$ (steady state for DC or rms for $A C$ ) flows through the circuit, the corresponding voltage $V_{1}$ and $V_{2}$ (indicated in circuits) are related as shown in Column I.
(2010)
$I \neq 0, V_{1}$ is proportional to $I$ (p)
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Answer:
Correct Answer: 8. $A \rightarrow r, s, t ; B \rightarrow q, r, s, t ; C \rightarrow q, p ; D \rightarrow q, r, s, t$
Solution:
- In circuit (p) I can’t be non zero in steady state.
In circuit (q) $V_{1}=0$ and $V_{2}=2 I=V$ (also)
In circuit (r) $V_{1}=X_{L} I=(2 \pi f L) I$
$$ \begin{aligned} & =\left(2 \pi \times 50 \times 6 \times 10^{-3}\right) I=1.88 I \\ V_{2} & =2 I \end{aligned} $$
In circuit (s) $V_{1}=X_{L} I=1.88 I$
$$ \begin{aligned} V_{2} & =X_{C} I=\frac{1}{2 \pi f C} I \\ & =\frac{1}{2 \pi \times 50 \times 3 \times 10^{-6}} \quad I=(1061) I \end{aligned} $$
In circuit (t)
$$ \begin{aligned} & V_{1}=I R=(1000) I \\ & V_{2}=X_{C} I=(1061) I \end{aligned} $$
Therefore, the correct options are as under
(A) $\rightarrow \mathrm{r}, \mathrm{s}, \mathrm{t}$
(B) $\rightarrow \mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{t}$
(C) $\rightarrow$ q or $\mathrm{p}, \mathrm{q}$
(D) $\rightarrow \mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{t}$
