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Chapter 4: Q34E (page 843)

When a resistor with resistance Ris connected to a 1.50-V flashlight battery, the resistor consumes 0.0625 W of electrical power. (Throughout, assume that each battery has negligible internal resistance.) (a) What power does the resistor consume if it is connected to a 12.6-V car battery? Assume that Rremains constant when the power consumption changes. (b) The resistor is connected to a battery and consumes 5.00 W. What is the voltage of this battery?

Short Answer

Expert verified
  1. The power consumed by the resistor when connected to 12.6 V car battery is 4.41W
  2. The voltage of the battery is 13.4V .

Step by step solution

01

  (a) Determination of the power consumed by the resistor when connected to 12.6 V car battery.

The resistance is constant in both cases, and the expression of power is

p=V2R

Rearrange for R,

p=V2R

So, for equal resistance,

V12P1=V12P2....(1)SolveforP2,P2=V22P1V125

Substitute all the values in the above equation,

P2=(0.0625W)12.5V1.50V2=4.41W

02

(b) Determination of the voltage of the battery.

From equation (i), Solve for V2 as,

V12P1=V22P2V2=V1P2P1

Substitute all the values in the above equation,

V2=(1.50V)5.00W0.0625W=13.4VThus,thevoltageis13.4V.

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