Answer :
Final answer:
The terminal potential difference of a battery with an emf of 24 V and a 6-Ω resistor with a 3 A current flowing through it is 6 V, as calculated by subtracting the voltage drop across the resistor from the battery's emf.
Explanation:
The question involves calculating the terminal potential difference across a battery when it is connected to a resistor. The battery has an electromotive force (emf) of 24 V and is connected to a 6-Ω resistor. With a current of 3 A flowing through the resistor, we can use Ohm's Law and the definition of terminal potential difference to find the answer.
Terminal potential difference (V) is given by the equation V = emf - Ir, where I is the current and r is the internal resistance of the battery. Using the given values:
V = 24 V - (3 A)(r)
To find the terminal potential difference, we need to identify the internal resistance of the battery. Since the current is 3 A and the resistor is 6-Ω, a voltage drop of VR = I × R occurs across the resistor, which is:
VR = (3 A)(6 Ω) = 18 V
Since the entire voltage of the battery is not dropped across the resistor, the difference in voltage must account for the internal resistance of the battery. Thus:
V = 24 V - 18 V = 6 V
Therefore, the terminal potential difference of the battery is 6 V, which corresponds to option B.
