Question

A battery has emf E and internal resistance r = 1.50 Ω. A 14.0 Ω resistor is connected to the battery, and the resistor consumes electrical power at a rate of 92.0 J/s. What is the emf of the battery?

Answer 1

Answer:

E = 39.68 V

Explanation:

EMF ( Electromotive force) : This is defined as the magnitude of the potential difference of both the external circuit and the inside of the cell. The S.I unit is Volt.

The Expression for E.M.F is given as,

E = I(R+r) ................... Equation 1

Where E = EMF, I = current, R = External Resistance, r = internal resistance.

Also,

P = I²R

I = √(P/R) ..................... Equation 2

Where P = power, R = External resistance.

Given: P = 92 J/s, R = 14 Ω.

Substitute into equation 2

I = √(92/14)

I = √(6.57)

I = 2.56 A.

Also Given: r = 1.5 Ω.

Substitute into equation 1

E = 2.56(1.5+14)

E = 2.56(15.5)

E = 39.68 V.