A battery closed to 4 Ohm will give a current of 2A. Also, closed to 9 Ohm will give a current of 1A. What is the short circuit current?

From the condition it is known that a battery closed by 4 ohms will give a current of 2 A. It is also closed by 9 ohms will give a current of 1 A. Find out what is the short-circuit current equal to?

Let’s write it down:

R1 = 4 ohms;

R2 = 9 ohms;

I1 = 2 A;

I2 = 1 A.

Find: Ik -?.

Decision:

To solve, we apply the formula:

I = E / (R + r);

We express the electromotive force from the formula:

E = I * (R + r).

For a given battery, we have the expression:

I1 * R1 + I1 * r = I2 * R2 + I2 * r.

We express r:

r = (I2 * R2 – I1 * R1) / (I1 – I2) = 1 ohm.

In the absence of external resistance, apply the formula:

E = 10V;

Ik = E / r = 10 A.