Question

Four resistors each of 22 are connected in the form of four sides of a parallelogram. The equivalent resistance between any two opposite corners is

• A. 1 Ω
• B. 2 Ω
• C. 4 Ω
• D. 8 Ω

Answer 1

The Correct Option is B

In this problem, four resistors are arranged in the shape of a parallelogram.
The resistors are of equal value \( 2 \, \Omega \), and we are asked to determine the equivalent resistance between two opposite corners.
We can simplify the problem by observing that the resistors can be grouped into two sets of parallel resistors.
Let’s label the resistors as \( R_1, R_2, R_3, R_4 \), each with a resistance of \( 2 \, \Omega \).
Resistors \( R_1 \) and \( R_3 \) are in parallel.
Resistors \( R_2 \) and \( R_4 \) are also in parallel.
The formula for two resistors in parallel is: \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} \] For \( R_1 = R_3 = 2 \, \Omega \): \[ \frac{1}{R_{\text{parallel1}}} = \frac{1}{2} + \frac{1}{2} = 1 \quad \Rightarrow \quad R_{\text{parallel1}} = 1 \, \Omega \] For \( R_2 = R_4 = 2 \, \Omega \): \[ \frac{1}{R_{\text{parallel2}}} = \frac{1}{2} + \frac{1}{2} = 1 \quad \Rightarrow \quad R_{\text{parallel2}} = 1 \, \Omega \] Now, the two parallel resistors are in series, and the total equivalent resistance is the sum of these two resistances: \[ R_{\text{eq}} = R_{\text{parallel1}} + R_{\text{parallel2}} = 1 + 1 = 2 \, \Omega \]

The correct option is (B): \(2\ Ω\)