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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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Most popular questions from this chapter

The switch in FIGURE CP28.80 has been closed for a very long time.

a. What is the charge on the capacitor?

b. The switch is opened at t = 0 s. At what time has the charge on the capacitor decreased to 10% of its initial value?

What is the equivalent resistance between points a and b in FIGURE EX28.25?

A 12 V car battery dies not so much because its voltage drops but because chemical reactions increase its internal resistance. A good battery connected with jumper cables can both start the engine and recharge the dead battery. Consider the automotive circuit of FIGURE P28.65.

a. How much current could the good battery alone drive through the starter motor?

b. How much current is the dead battery alone able to drive through the starter motor?

c. With the jumper cables attached, how much current passes through the starter motor?

d. With the jumper cables attached, how much current passes through the dead battery, and in which direction?

The switch in FIGURE EX28.36 has been in position a for a long time. It is changed to position b att=0 . What are the charge Qon the capacitor and the current Ithrough the resistor (a)immediately after the switch is closed? (b)att=50渭s ? (c)at t=200渭s?

A circuit you鈥檙e building needs an ammeter that goes from 0mAto a full-scale reading of 50mA. Unfortunately, the only ammeter in the storeroom goes from 0渭础to a full-scale reading of only 500渭础. Fortunately, you鈥檝e just finished a physics class, and you realize that you can make this ammeter work by putting a resistor in parallel with it, as shown in FIGURE P28.57. You鈥檝e measured that the resistance of the ammeter is50鈩�, not the0鈩�of an ideal ammeter.

a. What value of R must you use so that the meter will go to full scale when the current I is50mA?

b. What is the effective resistance of your ammeter?
See all solutions

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