Class 4 (4th Engineer) MET 📅 Apr 2024

Exam Question

A 24V emergency battery is to be charged from the 11OV ship's mains when the e.m.f. per cell has fallen to a minimum value of 1.8V. The battery consists of 12 cells in series, has a capacity of 100 Ahr at a 10 hr rate and the internal resistance is 0.03Ω/cell. If charging continues untill the voltage per cell rises to 2.2V, find the value of the variable resistor needed to control the charging. The charging current can be assumed to be equal to the maximum allowable discharge current.

Reference Answer

### Principle
This problem involves calculating the required series resistance to charge a battery from a DC source with a higher voltage. The key principle is applying Kirchhoff's Voltage Law (KVL) to the charging circuit. The source voltage must overcome the battery's back electromotive force (e.m.f.) and also account for the voltage drops across both the battery's internal resistance and the external variable resistor.
The charging current is kept constant. As the battery charges, its back e.m.f. increases. To maintain a constant current, the total resistance in the circuit must be decreased. Therefore, the external variable resistor must be adjusted from a maximum value at the start of the charge to a minimum value at the end of the charge.
### Given Data

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