A battery of emf 5 V and internal resistance 2.0 ohm is connected to an external resistance . If the current in the circuit is 0.4 A, the terminal voltage of the battery is :

To find the terminal voltage of a battery when it is connected to an external resistance, we can use a straightforward formula that takes into account the electromotive force (emf) of the battery, its internal resistance, and the current flowing through the circuit. Let's break this down step by step.

Understanding the Components

In this scenario, we have:

• Emf (E): This is the voltage provided by the battery, which is 5 V.
• Internal Resistance (r): This is the resistance within the battery itself, given as 2.0 ohms.
• Current (I): The current flowing through the circuit is 0.4 A.

Calculating the Voltage Drop

The terminal voltage (V) of the battery can be calculated using the formula:

V = E - I × r

Here, I × r represents the voltage drop across the internal resistance of the battery. This drop occurs because some of the voltage is used to overcome the internal resistance when current flows.

Plugging in the Values

Now, let's substitute the known values into the formula:

• Emf (E) = 5 V
• Current (I) = 0.4 A
• Internal Resistance (r) = 2.0 ohms

Calculating the voltage drop:

I × r = 0.4 A × 2.0 ohms = 0.8 V

Finding the Terminal Voltage

Now we can find the terminal voltage:

V = 5 V - 0.8 V = 4.2 V

Final Result

The terminal voltage of the battery, when a current of 0.4 A is flowing through it, is 4.2 V. This value indicates the actual voltage available at the terminals of the battery for the external circuit, which is less than the emf due to the internal resistance.

Understanding this concept is crucial, especially in practical applications where internal resistance can significantly affect the performance of batteries in circuits. If you have any further questions or need clarification on any part of this, feel free to ask!