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Chapter 30: Q. 34 (page 871)

What value of resistor $R$ gives the circuit in FIGURE $EX 30.34$ a time constant of $25 μs$ $?$

Short Answer

Expert verified

Value of resistor with time constant $25 μs$ is $750 Ω$ .

Step by step solution

01

Formula for current decays and equivalent resistance

In a circuit, current decays through an inductor, and the time constant is given by

$τ = \frac{L}{R_{eq}} . . . . . . . . . . 1$

R_{eq}

is the circuit's equivalent resistance

localid="1648830639011" $R_{eq} = \frac{L}{τ} . . . . . . 2$

02

Calculation for resistance value

$L = 7.5 \times 10^{- 3} H$

$t = 25 \times 10^{- 6} s$

All values should be substituted,

$R_{eq} = \frac{L}{τ} = \frac{7.5 \times 10^{- 3}}{25 \times 10^{- 6} s} = 300 Ω$

The two resistors $500 Ω$ and $R$ They are linked in a series.

Simultaneously, the corresponding resistance is equal to

$R = {(\frac{1}{R_{eq}} - \frac{1}{500 Ω})}^{- 1}$

$= {(\frac{1}{300 Ω} - \frac{1}{500 Ω})}^{- 1}$

$= 750 Ω$

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Most popular questions from this chapter

I Electricity is distributed from electrical substations to neighborhoods at 15,000 V. This is a $60 Hz$ oscillating $(AC)$ voltage. Neighborhood transformers, seen on utility poles, step this voltage down to the $120 V$ that is delivered to your house.

a. How many turns does the primary coil on the transformer have if the secondary coil has 100 turns?

b. No energy is lost in an ideal transformer, so the output power $P_{out}$ from the secondary coil equals the input power $P_{in}$ to the primary coil. Suppose a neighborhood transformer delivers $250 A$ at $120 V$ . What is the current in the $15, 000 V$ line from the substation?

$5.0 μ s$ after the switch of FIGURE is moved from $a$ to $b$ , the magnetic energy stored in the inductor has decreased by half. What is the value of the inductance $L$ ?

A small, 2.0-mm-diameter circular loop with $R = 0.020 Ω$ is at the center of a large 100-mm-diameter circular loop. Both loops lie in the same plane. The current in the outer loop changes from $+ 1.0 A$ to $- 1.0 A$ in $0.10 s$ . What is the induced current in the inner loop?

FIGURE shows a bar magnet, a coil of wire, and a current meter. Is the current through the meter right to left, left to right, or zero for the following circumstances? Explain.

a. The magnet is inserted into the coil.

b. The magnet is held at rest inside the coil.

c. The magnet is withdrawn from the left side of the coil.

An LC circuit has a 10 mH inductor. The current has its maximum value of 0.60 A at t = 0 s. A short time later the capacitor reaches its maximum potential difference of 60 V. What is the value of the capacitance?

See all solutions

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