The battery gives a current of 10 A, the voltage at its terminals is 12 V. How long will this battery

The battery gives a current of 10 A, the voltage at its terminals is 12 V. How long will this battery perform work in 1 kWh? What is the electromotive force of a battery if its internal resistance is 0.03 ohm?

I = 10 A.

U = 12V.

A = 1kW * h = 3600000 J.

r = 0.03 ohm.

t -?

EMF -?

Let us express the work of electric current A by the Joule-Lenz law: A = U * I * t, where U is the voltage at the battery terminals, I is the current in the circuit, t is the operating time of the battery.

t = A / U * I.

t = 3,600,000 J / 12 V * 10 A = 30,000 s = 8.33 h.

We express the EMF of the battery from Ohm’s law for a closed loop: EMF = I * (r + R), where r is the internal resistance of the battery, R is the external resistance of the circuit.

R = U / I – Ohm’s law for the circuit section.

EMF = I * (r + U / I).

EMF = 10 A * (0.03 Ohm + 12 V / 10 A) = 12.3 V.

Answer: the battery has an EMF = 12.3 V, t = 8.33 h.