Question

Find the equivalent resistance across A and B for given circuit.

• A. 6.4 Ω
• B. 4Ω
• C. 3.2Ω
• D. 8Ω

Hint:

For complex circuits, use series-parallel combinations or delta-star transforma tions to simplify the circuit before calculating the equivalent resistance.

Answer 1

The Correct Option is C

Step 1: Formula for Equivalent Resistance

For a balanced Wheatstone Bridge, the equivalent resistance between points \( a \) and \( b \) is given by:

\[ \frac{1}{R_{ab}} = \frac{1}{16} + \frac{1}{8} + \frac{1}{8} \]

Step 2: Simplify the Equation

Combine the terms by finding a common denominator:

\[ \frac{1}{R_{ab}} = \frac{1}{16} + \frac{2}{16} + \frac{2}{16} \]

\[ \frac{1}{R_{ab}} = \frac{5}{16} \]

Step 3: Find \( R_{ab} \)

Take the reciprocal to calculate \( R_{ab} \):

\[ R_{ab} = \frac{16}{5} = 3.2 \, \Omega \]

Final Answer:

The equivalent resistance between points \( a \) and \( b \) is:

\( R_{ab} = 3.2 \, \Omega \)