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Chapter 28: Q.70 (page 794)

A 50 mF capacitor that had been charged to 30 V is dis-charged through a resistor. FIG颅URE P28.70 shows the capacitor voltage as a function of time. What is the value of the resistance?

Short Answer

Expert verified

R=72.8惟

Step by step solution

01

Given information.

We need to find the values for R.

02

Simplification.

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 t.the initial voltage is related to the final voltage by

鈭�V=鈭�V0e-t/RC

where R is the resistance and Cis the capacitance. Let us solve equation (1) for localid="1649245722256" Rto get it by

R=-tCIn(鈭�V/Q鈭�V0)

At the time localid="1649245730682" t=4ms,the final voltage islocalid="1649245738870" 鈭�V=10v. We plug the values for localid="1649245747283" t,C,鈭�Vand 鈭�V0into equation to get R

R=-tCIn(鈭�V/Q鈭�V0)=-4脳10-3s(50脳10-6F)(In(10/30))=72.8惟.

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For the circuit shown in FIGURE P28.60, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading.

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