Q. 38 A capacitor is discharged throug... [FREE SOLUTION]

91影视

Chapter 28: Q. 38 (page 792)

A capacitor is discharged through a $100 惟$ resistor. The discharge current decreases to $25 %$ of its initial value in $2.5 m s$ . What is the value of the capacitor?

Short Answer

Expert verified

The value of capacitor is $18 渭 F$ .

Step by step solution

Given Information

We need to find the value of capacitor.

Simplify

When the switch is off, the capacitor-discharge, and the current flows through the resistor. To discharge the capacitor, the charges flow through the circuit in time $r$ . The initial current $I_{o}$ is related to the final charge $I$ by equation in the form

localid="1648921959204" $I = I_{o} e^{- t / R C} (1)$

Where $R$ is the resistance and $C$ is the capacitance. The initial current $I_{o}$ is reduced to its $25 %$ value, so the final current is

$I = 0.25 I_{o}$

After solving the equation $(1)$ for $C$ to be in the form

$Q = Q_{o} e^{- t / R C} I n (\frac{Q}{Q_{o}}) = \frac{- t}{R C} 鈥� (2) C = \frac{1}{R} (\frac{- t}{I n (Q / Q_{o})})$

Putting the values localid="1648922115145" $C, t a n d I = 0.25 I_{}$ into equation $(2)$ to get $R$

localid="1648922333327" $C = \frac{1}{R} (\frac{- t}{I n (I / I_{o})}) = \frac{1}{1000 惟} (\frac{- (2.5 脳 10^{- 3} s)}{I n (0.25 I_{o} / I_{o})}) = 18 脳 10^{- 6} F = 18 渭 F$