Question

Resistance of each side is $R$. Find equivalent resistance between two opposite points as shown in the figure. 

• A. $\dfrac{4}{5}R$
• B. $\dfrac{8}{5}R$
• C. $\dfrac{8}{10}R$
• D. $\dfrac{2}{5}R$

Hint:

In symmetric resistor networks, identify equipotential points to reduce the circuit easily.

Answer 1

The Correct Option is A

Step 1: Apply the concept of equipotential points

Due to the geometrical symmetry of the hexagonal network, pairs of opposite junctions are at the same potential.

Hence, no current flows through the resistors connecting these equipotential points, and they can be safely removed from the circuit.

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Step 2: Redraw the simplified network

After removing the zero-current branches, the remaining circuit reduces to two identical paths between the terminals.

Each path contains resistances that can now be combined using series and parallel rules.

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Step 3: Equivalent resistance of one path

Each simplified path consists of:

• One resistance of value R in series
• Two resistances of value R connected in parallel

Equivalent of the parallel part:

R_p = (R × R) / (R + R) = R / 2

Total resistance of one path:

R_path = R + R/2 = 3R/2

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Step 4: Combine the two identical paths

The two paths are in parallel, so:

1 / R_eq = 1 / (3R/2) + 1 / (3R/2)

1 / R_eq = 2 / (3R)

R_eq = 3R / 2 × 1/2 = 4R / 5

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Final Answer:

The equivalent resistance of the given network is
R_eq = (4/5)R