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Chapter 28: Q. 35 (page 792)

A 10渭Fcapacitor initially charged to 20渭Cis discharged through a 1.0k惟 resistor. How long does it take to reduce the capacitor鈥檚 charge to 10渭C?

Short Answer

Expert verified

t=6.9ms time will be taken to reduce the cpacitor's charge to10渭C.

Step by step solution

01

Given Information  

We need to find that how long does it take to reduce the capacitor鈥檚 charge to 10渭C.

02

Simplify

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 charge Qois related to the final charge Qby equation in the form

Q=Qoe-tRC (1)

Here, Ris the resistance and Cis the capacitance. Let us solve equation (1) to get it by

t=-RCInQQo (2)

Now, putting the values forR,C,Qand Qointo equation (2) to get t

t=-RCInQQo=-(1000)(10脳10-6F)In10渭C20渭C=6.9脳10-3s=6.9ms

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