For a real cell in a circuit, the terminal potential difference is at its closest to the emf when

The terminal potential difference in a real cell in a circuit is closest to the emf (electromotive force) when the current in the circuit is zero.

Here's why:

1. In a real cell, there is some internal resistance due to the materials and chemicals inside the cell. This internal resistance is in series with the load resistance (the rest of the circuit).

2. When current flows through the circuit, there is a voltage drop across this internal resistance (according to Ohm's law, V=IR). This means that the terminal voltage (the voltage across the cell terminals, which is what a voltmeter would measure) is less than the emf.

3. The terminal voltage is given by the equation V = E - Ir, where E is the emf, I is the current, and r is the internal resistance.

4. When the current I is zero (i.e., the circuit is open or the load resistance is very high), the term Ir becomes zero, and so the terminal voltage V equals the emf E.

So, the terminal potential difference is at its closest to the emf when the current in the circuit is zero.