Question

A wire of resistance R is connected across a cell of emf ε and internal resistance r. The current through the circuit is I. In time t, the work done by the battery to establish the current I is

• A. \(\frac{ε^2t}{R}\)
• B. IRt
• C. I²Rt
• D. εIt

Answer 1

The Correct Option is D

Step 1: Identify what's being asked clearly:

The question asks for the work done by the battery to establish a current \( I \) through the circuit in time \( t \).

Step 2: Recall the basic concept:

The work done (\( W \)) by a battery or cell to establish a current is given by:

\[ W = \text{EMF} \times \text{Charge} \]

Step 3: Determine the total charge moved by the battery in time \( t \):

The electric charge (\( Q \)) moved is given by:

\[ Q = I \times t \]

Step 4: Substitute this into the formula for work done:

\[ W = \varepsilon \times Q = \varepsilon \times I \times t \]

This gives the total work done by the battery as:

\[ W = \varepsilon I t \]

Important: The internal resistance \( r \) of the battery does not affect this direct formula for the work done by the battery. The battery always provides energy equal to its emf times the charge passed through it.

Final Answer: Option (D) \( \varepsilon I t \)

Answer 2

The work done by the battery to establish the current is given by the formula: \[ W = \varepsilon \times I \times t \] Where:
\( W \) is the work done,
\( \varepsilon \) is the emf of the battery,
\( I \) is the current,
\( t \) is the time.
Thus, the work done by the battery is \( \varepsilon It \).

Final Answer: Option (D) \(εIt\)