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?

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.