A circuit consists of a battery with an emf of 12 V and an internal resistance of 2.5 Ω connected in series to a resistor of 10 Ω. The circuit is completed with a switch. When the switch is closed, the electric current through the circuit is measured to be 1.5 A. Determine the potential difference across the resistor.
To find the potential difference across the resistor, we need to calculate the voltage drop across it.
First, let's calculate the total resistance of the circuit, which is the sum of the internal resistance of the battery and the resistance of the resistor:
Total Resistance (R_total) = Internal Resistance (R_internal) + Resistor Resistance (R_resistor) R_total = 2.5 Ω + 10 Ω R_total = 12.5 Ω
Now, we can use Ohm's Law, V = IR, to find the potential difference across the resistor. Rearranging the formula, we have:
V_resistor = I * R_resistor V_resistor = 1.5 A * 10 Ω V_resistor = 15 V
The potential difference across the resistor is 15 V.
Note: In this problem, the internal resistance of the battery was given to account for the voltage drop within the battery itself.