Question

A battery of 10V and internal resistance $0.5\Omega$ is connected across a variable resistance R. The value of R for which the power delivered is maximum is equal to

• A. $0.25\Omega$
• B. $0.5\Omega$
• C. $1\Omega$
• D. $2\Omega$

Answer 1

The correct option is B $0.5\Omega$

Given: A battery of $10V$ and internal resistance $0.5\Omega$ is connected across a variable resistance $R$

To find the value of R for which the power delivered is maximum

Solution:

The output power of a cell is given by

$P=I^{2}R$

$\therefore P=\frac{V^2}{(r+R{)}^2}R$

Maximum power is delivered to the load only when the internal resistance of the source is equal to the load resistance (R).

Hence, the value of R for which the power delivered is maximum = $0.5\Omega$