Twelve cells each of e.m.f. of 2V and of internal resistance 0.5 ohm are arranged in a battery on n rows and an external resistance 3/8 ohm is current through the resistance in terms of n. connected to the poles of the battery. Estimate the
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To find the current through the external resistance we can use Ohm's Law. Ohm's Law states that the current (I) flowing through a circuit is equal to the voltage (V) across the circuit divided by the total resistance (R) of the circuit. In this case the voltage is the sum of the voltages across the 12 cells and the total resistance is the sum of the internal resistance of the cells plus the external resistance.
Let's calculate the total voltage and total resistance:
Total voltage = 12 (number of cells) * 2V (emf per cell) = 24V
Total internal resistance = 12 (number of cells) * 0.5 ohm (internal resistance per cell) = 6 ohm
Total external resistance = 3/8 ohm
Total resistance of the circuit = Total internal resistance + Total external resistance
= 6 ohm + 3/8 ohm
= 6 ohm + 3/8 ohm
= 48/8 ohm + 3/8 ohm
= 51/8 ohm
Now we can use Ohm's Law to calculate the current (I) through the external resistance:
I = V / R
= 24V / (51/8 ohm)
To simplify the calculation let's convert the division into multiplication by taking the reciprocal of the denominator:
I = 24V * (8/51 ohm)
= (192/51) A
Hence the current through the external resistance in terms of n is approximately 3.7647A.