Question

A battery of e.m.f 10 V and internal resistance $0.5\, \Omega$ is connected across a variable resistance R. The value of R for which the power delivered in it is maximum is given by

• A. $0.5\, \Omega$
• B. $1.0\, \Omega$
• C. $2.0\, \Omega$
• D. $0.25\, \Omega$

Answer 1

The Correct Option is A

To find the value of the variable resistance \( R \) for which the power delivered to it is maximum, we need to apply the concept of maximum power transfer theorem. According to this theorem, maximum power is transferred to the load when the load resistance \( R \) is equal to the internal resistance \( r \) of the source. Let's analyze the given problem step-by-step:

1. According to the problem, the battery has an internal resistance \( r = 0.5\, \Omega \) and is connected across a variable resistance \( R \).
2. The electromotive force (e.m.f) of the battery is given as \( 10 \, V \).
3. For maximum power transfer, the condition \( R = r \) must be satisfied. Hence, the value of \( R \) should be equal to the internal resistance of the battery, which is \( 0.5\, \Omega \).

Therefore, under the condition for maximum power transfer, the optimum resistance value \( R \) is:

R = 0.5\ \Omega

Hence, the correct answer is $0.5\, \Omega$.

Let's briefly discuss why other options are not correct:

• $1.0\, \Omega$, $2.0\, \Omega$, and $0.25\, \Omega$ do not satisfy the condition \( R = r \), as the internal resistance is \( 0.5\ \Omega\).

Thus, among the provided options, $0.5\, \Omega$ is the correct choice because it meets the criterion for maximum power transfer.