Question: Four resistors, each of resistance $R$ and a key $K$ are connected as shown in the figure. The equivalent resistance between points A and B when key $K$ is open, will be:
Step 1 (Formula / Governing Law & Given Data): [0.25 Mark]
When the key $K$ is open, the circuit branch containing the key acts as an open circuit (infinite resistance). Consequently, no current flows through that branch. The remaining resistors form a series combination. The formula for equivalent resistance in series is:
$$R_{eq} = R_1 + R_2 + R_3 + ... + R_n$$Step 2 (Step-by-Step Mathematical Working): [0.5 Mark]
- When key $K$ is open, the path containing the key is disconnected.
- The circuit simplifies to four resistors of resistance $R$ connected in a single series path between points A and B.
- Substituting the values into the series resistance formula: $$R_{eq} = R + R + R + R$$ $$R_{eq} = 4R$$
Step 3 (Final Concluded Answer): [0.25 Mark]
The equivalent resistance between points A and B is $4R$. Therefore, the correct option is (A).
💡 EL10 Concept Insight: Imagine the resistors are like sections of a pipe connected in a single line; when the key is open, it's like a closed valve that stops water from taking a shortcut, forcing all the water to travel through every single pipe section one after another, adding up their total length.