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The circuit shown in the figure consists...

The circuit shown in the figure consists of a battery of emf `epsilon = 10 V` , a capacitor of capacitance `C = 1.0 mu F` and three resistors of value `R_(1) = 2 Omega, R_(2) = 2 Omega` and `R_(3) = 1 Omega`, Initially the capacitor is completely uncharged and the switch `S` is open. The switch `S` is closed at `t = 0`. Then

A

the current through resistor `R_3` at the moment the switch closed is zero

B

the current through resistor `R_3` a long time after the switch closed is 5A

C

the ratio of current through `R_1 and R_2` is always constant

D

all of these

Text Solution

Verified by Experts

The correct Answer is:
D
d. At `t = prop`, the equivalent circuit is

`:. I = (epsilon/(R_3 + (R_1R_2)/(R_1+R_2))) = 10 /(1+((2)(2))/(2+2)) = 10 /(1+1) = 5A`
Also, `I_(R_1) R_1 = I_(R_2) R_2 or I_(R_1)/I_(R_2) = R_2/R_1`
`:. V_(AB) = IR_3 = (5)(1) = 5V`
`:. Q_(max) = CV_(AB) = 5muC`
At t = 0, the equivalent circuit is

`:. I_(R_3) = 0`
and `I_(R_1)R_1 = I_(R_2) R_2 or I_(R_1)/I_(R_2) = R_2/R_1` .
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