A storage battery of emf 8.0 V and internal resistance 0.5 W is beingcharged by a 120 V dc supply using a series resistor of 15.5 W. Whatis the terminal voltage of the battery during charging? What is thepurpose of having a series resistor in the charging circuit?
Question
A storage battery of emf 8.0 V and internal resistance 0.5 W is beingcharged by a 120 V dc supply using a series resistor of 15.5 W. Whatis the terminal voltage of the battery during charging? What is thepurpose of having a series resistor in the charging circuit?
Solution
The terminal voltage of the battery during charging can be calculated using Ohm's law and the concept of voltage division in series circuits.
Step 1: Calculate the total resistance in the circuit. The total resistance (R_total) is the sum of the internal resistance of the battery (r), and the resistance of the series resistor (R).
R_total = r + R = 0.5 Ω + 15.5 Ω = 16 Ω
Step 2: Calculate the total current in the circuit. The total current (I) can be calculated using Ohm's law, V = IR, where V is the voltage supplied by the DC source.
Rearranging for I gives I = V / R_total = 120 V / 16 Ω = 7.5 A
Step 3: Calculate the terminal voltage of the battery. The terminal voltage (V_t) is the product of the current (I) and the sum of the internal resistance of the battery (r) and the emf of the battery (E).
V_t = I * (r + E) = 7.5 A * (0.5 Ω + 8 V) = 63.75 V
So, the terminal voltage of the battery during charging is 63.75 V.
The purpose of having a series resistor in the charging circuit is to limit the current flowing into the battery during charging. Without this resistor, the current could be high enough to damage the battery. The resistor also helps to dissipate heat generated during the charging process.
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