What will be the equivalent resistance between the two points A and D?

Question

What will be the equivalent resistance between the two points A and D? (A) 30 Ω (B) 40 Ω (C) 10 Ω (D) 50 Ω

Tardigrade Admin · Accepted Answer

Lower resistance on extreme left and upper resistance on extreme right are ineffective.
The resistance

R_{2}

and

R_{3}

are in series combination.
Therefore their equivalent resistance,

R^{'} = R_{2} + R_{3} = 10 + 10 = 20Ω

.
Similarly, the resistance

R_{5}

and

R_{6}

are in series combination.
Therefore their equivalent resistance,

R^{''} = R_{5} + R_{6} = 10 + 10 = 20Ω

.
Now the equivalent resistances

R^{'}

and

R^{''}

are in parallel combination.
Therefore their equivalent resistance.

R^{'''} = \frac{R ^{'} R ^{''}}{R ^{'} + R ^{''}} = \frac{20 \times 20}{20 + 20} = \frac{400}{40} = 10Ω

.
Thus equivalent resistance between

A

and

D, R = R_{1} + R^{'''} + R_{4} = 10 + 10 + 10 = 30Ω (∵

series combination)

Q. What will be the equivalent resistance between the two points $A$ and $D$ ?