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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

When the lights of a car are switched on, an ammeter in series with them reads10.0 Aand a voltmeter connected across them reads12.0 V(Fig. 27-60). When the electric starting motor is turned on, the ammeter reading drops to8.00 Aand the lights dim somewhat. If the internal resistance of the battery is0.0500 ohmand that of the ammeter is negligible, what are (a) the emf of the battery and (b) the current through the starting motor when the lights are on?

Question: In Figure,R1=R2=4.00ΩandR3=2.50Ω . Find the equivalent resistance between points D and E.

(Hint: Imagine that a battery is connected across those points.)

In Fig. 27-50, two batteries with an emfε=12.0 Vand an internal resistance r=0.200 Ωare connected in parallel across a resistance R. (a) For what value of Ris the dissipation rate in the resistor a maximum? (b) What is that maximum?

In Figure, ε1=6.00V, ε2=12.0V ,R1=100Ω , R2=200Ω ,andR3=300Ω . One point of the circuit is grounded(V=0) .(a)What is the size of the current through resistance 1? (b) What is the direction (up or down) of the current through resistance 1? (c) What is the size of the current through resistance 2?(d) What is the direction (left or right) of the current through resistance 2? (e) What is the size of the current through resistance 3? (f) What is the direction of the current through resistance 3? (g) What is the electric potential at point A?

A certain car battery with a 12.0 V emf has an initial charge of 120 A h. Assuming that the potential across the terminals stays constant until the battery is completely discharged, for how many hours can it deliver energy at the rate of 100 W?
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