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Chapter 32: Q. 23 (page 924)

The peak current through an inductor is 10mA. What is the peak current if

a. The emf frequency is doubled?

b. The emf peak voltage is doubled (at the original frequency)

Short Answer

Expert verified

(a) Current is 5mA

(b) Current is20mA

Step by step solution

01

Part (a) Step 1: Given information 

We have been given that,

Current through inductor isI0=10mA

02

Part (a) Step 2: Simplify

Let Voltage is V0

And Frequency is f0

And Inductance is L

And Inductive reactance is localid="1649934635236" XL=2πf0L

Therefore, Current is

I0=V02πf0LI0=V02πf0L

Now, Frequency is doubled i.e. f=2f0

Therefore, Current is,

localid="1649935758169" I=V02πfLI=V02π×2f0LI=I02I=102I=5mA

Hence, Current is 5mA

03

Part (b) Step 1: Given information 

We have been given that,

Current through inductor isI0=10mA

04

Part (b) Step 2: Simplify

Let Voltage isV0

And inductive reactance isXL

Therefore, Current is

I0=V0XL

Now, Voltage isV=2V0

Therefore, Current is,

I=VXLI=2V0XLI=2I0I=2×10I=20mA

Hence, current is20mA

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Most popular questions from this chapter

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf, three separate wires carry currents for the emfs E1=E0cosvt,E2=E0cos1vt+120°,andE3=E0cos1vt-120°over three parallel wires, each of which supplies one-third of the power. This is why the long-distance transmission lines you see in the countryside have three wires. Suppose the transmission lines into a city supply a total of 450MWof electric power, a realistic value.

a. What would be the current in each wire if the transmission voltage were E0=120Vrms?

b. In fact, transformers are used to step the transmission-line voltage up to 500kVrms. What is the current in each wire?

c. Big transformers are expensive. Why does the electric company use step-up transformers?

For a series RLC circuit, show that

a. The peak current can be written I=Imaxcosϕ.

b. The average power can be writtenPsource=Pmaxcos2ϕ.

The resonance frequency of a series RLC circuit is less than the EMF frequency. Does the current lead or lag the EMF? Explain.

A series RLcircuit is built with a role="math" localid="1650111235060" 110Ωresistor and a 5.0-cm- long,1.0-cm-diameter solenoid with 800turns of wire. What is the peak magnetic flux through the solenoid if the circuit is driven by a 12V,5.0kHzsource?

FIGURE Q32.1shows emf phasors a, b, and c.

a. For each, what is the instantaneous value of the emf?

b. At this instant, is the magnitude of each emf increasing, decreasing, or holding constant?
See all solutions

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