Given, $$\begin{array}{ll} \mathrm{R}_{1}=1 \Omega & \mathrm{C}_{1}=2 \mu \mathrm{~F} \\ \mathrm{R}_{2}=2 \Omega & \mathrm{C}_{2}=4 \mu \mathrm{~F} \end{array}$$ (I) (II) (III) The time constants (in $\mu \mathrm{S}$) for the circuits I, II, III are respectively

JEE Advanced · 2006 · 09 Apr 2006 · Current Electricity

Given,

R_{1} = 1Ω R_{2} = 2Ω C_{1} = 2 μ F C_{2} = 4 μ F

(I)

(II)

(III)

The time constants (in

μ S

) for the circuits I, II, III are respectively

(A)18, 8/9, 4
(B)18, 4, 8/9
(C)4, 8/9, 18
(D)8/9, 18, 4✓ Correct

Answer: (D)

Solution

For RC circuits, the time constant is

τ = R C_{e q}

where

C_{e q}

depends on the series/parallel combination.

For circuit I: The equivalent capacitance and resistance give

τ_{1} = 8/9 μ s

.

For circuit II:

τ_{2} = 18 μ s

.

For circuit III:

τ_{3} = 4 μ s

.

Therefore, the time constants are 8/9, 18, 4 in that order, which is option (D).

JEE Advanced · 2006 · 09 Apr 2006 · Single correct option

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