A battery of emf 10 V and internal resistance 3 O is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

To find the resistance of the resistor and the terminal voltage of the battery in this circuit, we can use Ohm's Law and the formula for terminal voltage. Let's break it down step by step.

Finding the Resistance of the Resistor

We know the following values:

• Electromotive force (emf) of the battery, E = 10 V
• Internal resistance of the battery, r = 3 Ω
• Current in the circuit, I = 0.5 A

According to Ohm's Law, the voltage across a resistor can be calculated using the formula:

V = I × R

In this case, the total voltage provided by the battery is used to overcome both the internal resistance of the battery and the resistance of the external resistor (R). The relationship can be expressed as:

E = I × (R + r)

Substituting the known values into the equation:

10 V = 0.5 A × (R + 3 Ω)

Now, let's solve for R:

First, divide both sides by 0.5 A:

20 V = R + 3 Ω

Next, isolate R:

R = 20 V - 3 Ω

R = 17 Ω

Calculating the Terminal Voltage

Now that we have the resistance of the resistor, we can find the terminal voltage of the battery when the circuit is closed. The terminal voltage (V_t) can be calculated using the formula:

V_t = E - I × r

Substituting the known values:

V_t = 10 V - (0.5 A × 3 Ω)

Calculating the product:

V_t = 10 V - 1.5 V

V_t = 8.5 V

Summary of Results

To summarize:

• The resistance of the resistor is 17 Ω.
• The terminal voltage of the battery when the circuit is closed is 8.5 V.

This analysis shows how the internal resistance of a battery affects the voltage available to external components in a circuit. Understanding these principles is crucial for working with electrical systems effectively.