Question

A battery with an emf of 12.0 V has a terminal voltage of 11.5 V when the current is 3.00 A.

(a) Calculate the battery's internal resistance r.
(b) Find the load resistance R.

Answer 1

Step-by-step explanation:

We can use Ohm's law and Kirchhoff's voltage law to solve for the battery's internal resistance and the load resistance.

(a) To calculate the internal resistance r of the battery, we can use the following equation:

V = EMF - Ir

Where:

V = terminal voltage

EMF = electromotive force (or voltage) of the battery

I = current

r = internal resistance

Substituting the given values, we get:

11.5 V = 12.0 V - 3.00 A x r

Solving for r, we get:

r = (12.0 V - 11.5 V) / 3.00 A ≈ 0.167 Ω

Therefore, the battery's internal resistance is approximately 0.167 Ω.

(b) To find the load resistance R, we can use Ohm's law:

V = IR

Where:

V = terminal voltage

I = current

R = load resistance

Substituting the given values, we get:

11.5 V = 3.00 A x R

Solving for R, we get:

R = 11.5 V / 3.00 A ≈ 3.83 Ω

Therefore, the load resistance is approximately 3.83 Ω.