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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. FIGURE P28.70 shows the capacitor voltage as a function of time. What is the value of the resistance?

Short Answer

Expert verified

$R = 72.8 Ω$

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

$∆ V = ∆ V_{0} e^{- t / R C}$

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

$R = \frac{- t}{C I n (∆ V / Q ∆ V_{0})}$

At the time localid="1649245730682" $t$ = $4 m s$ ,the final voltage islocalid="1649245738870" $∆ V = 10 v$ . We plug the values for localid="1649245747283" $t$ , $C, ∆ V$ and $∆ V_{0}$ into equation to get R

$R = \frac{- t}{C I n (∆ V / Q ∆ V_{0})} = \frac{- 4 \times 10^{- 3} s}{(50 \times 10^{- 6} F) (I n (10 / 30))} = 72.8 Ω$ .

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Most popular questions from this chapter

What is the time constant for the discharge of the capacitors in FIGURE EX28.34?

It seems hard to justify spending $\(4.00$ for a compact fluorescent lightbulb when an ordinary incandescent bulb costs $50 ¢$ . To see if this makes sense, compare a $60 W$ incandescent bulb lasting $1000$ hours to a $15 W$ compact fluorescent bulb having a lifetime of $10, 000$ hours. Both bulbs produce the same amount of visible light and are interchangeable. If electricity costs $\) 0.10 / kWh$ , what is the total cost—purchase plus energy— to obtain $10, 000$ hours of light from each type of bulb? This is called the life-cycle cost.

What are the battery current $I_{bat}$ and the potential difference $V_{a} - V_{b}$ between points a and b when the switch in FIGURE P28.55 is (a) open and (b) closed?

Bulbs A and B in FIGURE Q28.11 are identical, and both are glowing. Bulb B is removed from its socket. Does the potential difference $∆ V_{12}$ between points 1 and 2 increase, stay the same, decrease, or become zero? Explain.

What is the value of resistor $R$ in FIGURE $E X 28.16$ ?

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