Answer :
To determine the potential difference between two points on a wire, one can calculate the voltage drop per meter (2V/meter) and then find the drop over the desired distance (0.5 meters). Thus, the potential difference across 50 cm of the wire connected to a 6V battery with 100Ω resistance is 1V. Option d is correct.
The question is asking to calculate the potential difference (voltage) between two points on a 3-meter long wire, which has a total resistance of 100Ω and is connected to a 6V battery. We can use Ohm's law (V=IR) to find the voltage drop over a particular length of the wire.
Since the resistance is uniform along the wire's length, we can calculate the voltage drop per meter by dividing the total voltage by the total length of the wire. The voltage drop over 50 cm (0.5 meters) would be a fraction of the total voltage drop across the wire. The calculation is as follows:
Total voltage drop (V) = Resistance (R) x Current (I)
6V = 100Ω x I
Thus, Current (I) = 6V / 100Ω = 0.06A
Voltage drop per meter = Total voltage / Total length
Voltage drop per meter = 6V / 3m = 2V/meter
Therefore, the voltage drop over 50 cm = 2V/meter x 0.5 meters = 1V
The potential difference between two points on the wire separated by a distance of 50 cm will be 1V, which corresponds to option (d).
