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 $AC$ voltage source of $50 Hz$ 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) $\rightarrow r, s, t$
(B) $\rightarrow q, r, s, t$
(C) $\rightarrow$ q or $p, q$
(D) $\rightarrow q, r, s, t$
