Physics Q36 – JEE-MAIN 2025

Home Physics Current ElectricityQuestion #59

A wire of resistance

R

is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is

R / n

. The value of

n

is :

Clue 1 of 3: Identify Symmetry

Look for planes or axes of symmetry in the circuit diagram. This can help simplify the circuit by identifying equipotential points or branches with no current.

🧠 Full Solution Path

Step 1: Identify Symmetry and Simplify the Circuit✦ Active

The given circuit is a triangular pyramid (tetrahedron) with 6 identical resistors, each of resistance $r$ . Points A and B are at the base. Let the other two vertices be C and D. Due to the symmetry of the tetrahedron with respect to the input/output terminals A and B, the potentials at the two apex points C and D are equal, i.e., $V_{C} = V_{D}$ . This implies that no current flows through the resistor connecting C and D. Therefore, the resistor CD can be removed from the circuit without affecting the equivalent resistance between A and B.

Step 2: Calculate Equivalent Resistance of the Simplified Circuit○ Expand

After removing the resistor CD, the circuit consists of three parallel paths between A and B:

1. The direct path A-B with resistance $r$ .

2. The path A-C-B with total resistance $r + r = 2 r$ (resistors AC and CB are in series).

3. The path A-D-B with total resistance $r + r = 2 r$ (resistors AD and DB are in series).

The equivalent resistance $R_{A B}$ is given by the parallel combination of these three paths:

\frac{1}{R_{A B}} = \frac{1}{r} + \frac{1}{2 r} + \frac{1}{2 r}

\frac{1}{R_{A B}} = \frac{1}{r} + \frac{2}{2 r} = \frac{1}{r} + \frac{1}{r} = \frac{2}{r}

R_{A B} = \frac{r}{2}

Step 3: Determine the Value of n○ Expand

The total resistance of the wire is $R$ . Since there are 6 segments, each of resistance $r$ , the total resistance is $R = 6 r$ .

We are given that the resistance between points A and B is $R / n$ . So, we have:

R_{A B} = \frac{R}{n}

Substitute the values of $R_{A B}$ and $R$ :

\frac{r}{2} = \frac{6 r}{n}

Solving for $n$ :

\frac{1}{2} = \frac{6}{n} ⟹ n = 12

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Physics Question 36 – JEE-MAIN 2025

Clue 1 of 3: Identify Symmetry

🧠 Full Solution Path