Determine the internal resistance of a car battery with an emf of 12 V if the voltage at its terminals

Determine the internal resistance of a car battery with an emf of 12 V if the voltage at its terminals drops to u = 4.0 V when the starter is turned on, which consumes a current of I = 40A.

Let’s write down briefly given:

car battery with EMF 12;

U = 4.0V;

I = 40 A.

Find: r -?

Let’s apply Ohm’s law to the complete circuit.

Ohm’s law for a complete circuit – the current in the circuit is proportional to the emf acting in the circuit and is inversely proportional to the sum of the resistances of the circuit and the internal resistance of the source.

In the form of a formula, this can be written as:

I = E / (R + r),

where

R – load resistance,

r – internal resistance,

E – emf.

Let us express the internal resistance from the formula:

r = E / (I – R);

U = I * R;

R = U / I.

We get the formula:

r = E / I – U / I = (E – U) / I = (12 – 4.0) / 40 = 8/40 = 1/5 = 0.2 Ohm.