Answer :
To calculate the external resistance needed to charge a battery with 20 cells at 15 A and 220 V, we use Ohm's law. The total e.m.f. is 36 V, and the total internal resistance is 2 Ω. The external resistance required is 12.67 Ω.
The subject is physics, specifically involving concepts of electricity and circuits. In the given scenario, the student is asked to calculate the resistance to be put in a circuit for charging a battery with a specific current and voltage. The battery consists of 20 cells, each with an e.m.f. (electromotive force) of 1.8 V and internal resistance of 0.1
Ω. The total e.m.f. of the battery is the sum of the individual cells' e.m.f., which is 20
× 1.8 V = 36 V. The total internal resistance is the sum of the individual cells' internal resistance, which is 20
× 0.1 Ω = 2 Ω. When charging the battery with a 220 V supply at a current of 15 A, we can use Ohm's law to find the external resistance required.
To find the total resistance in the circuit (Rtotal) during charging, we use Ohm's law (
V = IR). We know that V (the supply voltage) is 220 V, I (the current during charging) is 15 A, and the total resistance will be the sum of the battery's internal resistance (rtotal) and the external resistance (R). Hence, the equation becomes:
220 V = 15 A × (R + rtotal)
First, let's solve for R + rtotal:
R + rtotal = 220 V / 15 A = 14.67 Ω
We already calculated the total internal resistance of the battery (rtotal) to be 2 Ω, so the external resistance (R) needed is:
R = 14.67 Ω - 2 Ω = 12.67 Ω
Therefore, an external resistance of 12.67 Ω needs to be added to the circuit for charging the battery at the specified current.