Question:

A student sets up a circuit as shown below. A battery with an emf (electromotive force) of 12V is connected to a resistor with a resistance of 4Ω. The circuit is closed and a current of 3A flows through the circuit.

a) According to Ohm's law, what is the potential difference across the resistor? b) What would be the current flowing through the circuit if the resistance of the resistor is doubled?

Answer:

a) According to Ohm's law, the potential difference across a resistor is given by the equation:

Where:

• V is the potential difference (Voltage) across the resistor in volts (V)
• I is the current flowing through the circuit in amperes (A)
• R is the resistance of the resistor in ohms (Ω)

Given that the current flowing through the circuit is 3A and the resistance of the resistor is 4Ω, we can substitute these values into the equation to find the potential difference across the resistor:

Therefore, the potential difference across the resistor is 12V.

b) If the resistance of the resistor is doubled, according to Ohm's law, the current flowing through the circuit can be found using the equation:

Where V is the potential difference (Voltage) across the resistor in volts (V), and R is the resistance of the resistor in ohms (Ω).

Given that the potential difference across the resistor is 12V and the resistance of the resistor is doubled to 8Ω, we can substitute these values into the equation to find the new current:

Therefore, if the resistance of the resistor is doubled, the current flowing through the circuit would be 1.5A.