CBSE Class 10 Answered

Let us connect a battery of potential difference V across the terminals A and B as shown in above figure.

Let the current distribution in the resistor network be as shown in above figure.

Let us apply Kirchoff's voltage law to the loop ACDA , then we get

From above equaltion , we get   ...............(1)

Let us apply Kirchoff's voltage law to the loop CBDC , then we get

From above equation , we get ,   ....................(2)

Let us apply Kirchoff's current law to the junction C , then we get

..........................(3)

using eqn.(2) , we rewrite eqn.(3) as   ...................(4)

using eqn.(4) , we rewrite eqn.(1) as    .....................(5)

If we apply Kirchoff's voltage law to the loop ADBA ( this loop is through battery ) , then we get

Hence

by substituting in eqn.(5) , we get 

by substituting in eqn.(5) , we get

Current derived from battery is ,

 Hence effective resistance of given network of resistors  = V / i = 6 Ω