Question

Three resistances of \(4\Omega\) each are connected as shown in figure. If the point D divides the resistance into two equal halves, the resistance between point A and D will be

• A. \(12\Omega\)
• B. \(6\Omega\)
• C. \(3\Omega\)
• D. \(\frac{1}{3}\Omega\)

Hint:

When two equal resistances are in parallel, their equivalent is half of one: \(6\parallel 6 = 3\Omega\).

Answer 1

The Correct Option is C

Step 1: Identify the circuit structure.
The circuit is a triangle with resistors \(4\Omega\) on all three sides (AB, AC, BC).
Point D is the midpoint of BC, meaning BC is divided into \(2\Omega\) and \(2\Omega\).
Step 2: Find resistance between A and D.
From A to D there are two paths:
Path 1: \(A \to B \to D\)
\[ R_1 = 4\Omega + 2\Omega = 6\Omega \]
Path 2: \(A \to C \to D\)
\[ R_2 = 4\Omega + 2\Omega = 6\Omega \]
Step 3: These two paths are in parallel.
\[ R_{AD} = \frac{R_1R_2}{R_1+R_2} = \frac{6\times 6}{6+6} = \frac{36}{12} = 3\Omega \]
Final Answer:
\[ \boxed{3\Omega} \]