A battery is connected across a series combination of two identical resistors. If the potential? difference across the terminals is V and the current in the battery is i, then:?

Question

Answer

The potential difference across each resistor is V/2 and the current in each resistor is i.

Answer

Explanation of the potential difference and current in a series combination of two identical resistors connected to a battery

When a battery is connected across a series combination of two identical resistors, the potential difference across the terminals is V and the current in the battery is i. This can be explained as follows:

Ohm's Law

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. This can be expressed mathematically as:

i = V/R

where i is the current through the conductor, V is the voltage across the two points, and R is the resistance of the conductor.

Series Combination of Resistors

In a series combination of two identical resistors, the resistors are connected end-to-end, so that the current flows through one resistor and then through the other. The total resistance of the series combination is the sum of the two resistances:

R = R1 + R2

where R1 and R2 are the resistances of the two identical resistors.

Potential Difference Across the Terminals

The potential difference across the terminals of the series combination of resistors is equal to the sum of the potential differences across each resistor:

V = V1 + V2

where V1 and V2 are the potential differences across each resistor.

Since the two resistors are identical, the potential difference across each resistor is equal:

V1 = V2 = V/2

Therefore, the potential difference across the terminals of the series combination of resistors is:

V = V1 + V2 = V/2 + V/2 = V

Current in the Battery

The current in the battery can be calculated using Ohm's law:

i = V/R = V/(R1 + R2) = V/(2R)

Since the two resistors are identical, R1 = R2 = R/2, and the total resistance is R = R1 + R2 = R/2 + R/2 = R:

i = V/R = V/(2R/2) = V/R

Therefore, the current in the battery is:

i = V/R

Conclusion

In a series combination of two identical resistors connected to a battery, the potential difference across the terminals is equal to the voltage of the battery, and the current in the battery is equal to the voltage of the battery divided by the resistance of the series combination of resistors.

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