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Chapter 27: Q21P (page 796)

Question: Four 18.0 Ω resistors are connected in parallel across a 25.0 V ideal battery. What is the current through the battery?

Short Answer

Expert verified

Answer

The value of the current isI=5.56A .

Step by step solution

01

Write the given data:

  1. The value of each resistor isR=18.0Ω
  2. The potential of the battery isV=25.0V
02

Determine the concept

Use the concept of Ohm’s law and the equivalent resistance of the parallel circuit. First, find the equivalent resistance and then, using that value in Ohm’s law formula, find the current through the battery.

Write the formula for the Ohm’s law and the equivalent resistance as:

V=IR1Req=1R1+1R2+1R3+1R4

03

Calculate the current through the battery  

First, calculate the equivalent resistance as follows:

1Req=118+118+118+118=4181Req=418Req=184Req=4.5Ω

Using this value in Ohm’s law formula and solve as:

V=IRI=VRI=25.04.50I=5.56A

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Most popular questions from this chapter

The circuit of Fig. 27-75 shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, what is the change in the charge on the capacitor? Assume,C=10μF,ε1=1.0V ,ε1=3.0V , R1=0.20ΩandR2=0.40Ω.

A simple ohmmeter is made by connecting a 1.50 Vflashlight battery in series with a resistanceRand an ammeter that reads from 0 to1.00 mA, as shown in Fig. 27-59. ResistanceRis adjusted so that when the clip leads are shorted together, the meter deflects to its full-scale value of1.00mA. What external resistance across the leads results in a deflection of (a) 10.0%, (b) 50.0%, and (c) 90.0%of full scale? (d) If the ammeter has a resistance of20.0Ωand the internal resistance of the battery is negligible, what is the value ofR?

In Fig. 27-66 R1=10.0KΩ,R2=15.0KΩ,C=0.400μFand the ideal battery has emf ε=20.0V. First, the switch is closed a longtime so that the steady state is reached. Then the switch is opened at time. What is the current in resistor 2 at t =4.00ms?

Question: You are given a number of10Ωresistors, each capable of dissipating only 1.0 W without being destroyed. What is the minimum number of such resistors that you need to combine in series or in parallel to make a10resistance that is capable of dissipating at least 5.0 W?

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