Electric Circuit

1. Identify the components and their configuration:
The circuit consists of:

• A resistor ( )
• A resistor ( )
• A resistor with unknown resistance R
• A voltage source V

The and resistors are connected in parallel. This parallel combination is connected in series with the resistor R. The total equivalent resistance of the circuit ( ) is given as .

2. Calculate the equivalent resistance of the parallel combination:
Let be the equivalent resistance of the parallel combination of and . The formula for the equivalent resistance of two parallel resistors is: $ ) is connected in series with the resistor R. The total equivalent resistance ( ) is the sum of resistances in series: \) . Substituting the known values into the equation from Step 3: \) from both sides to find R: \) . This corresponds to option (3).

Final Answer:

The final answer is \) {7 \Omega}$

To solve the problem, we need to understand the role of a fuse in a circuit.

1. Function of a Fuse:
A fuse is a safety device used in electrical circuits to protect against overload and short circuits. It contains a wire that melts when the current exceeds a certain limit, breaking the circuit and preventing further damage.

2. Effect of Overload:
In the case of an overload (when the current exceeds the safe limit), the fuse will blow, preventing further damage to the circuit and other components.

Final Answer:
The usage of a fuse in a circuit prevents .