Question

Find the equivalent resistance between the points P and Q in the given circuit and current through the resistance of 25 ohm.

Answer 1

Equivalent Resistance is 52.5ohm

Answer 2

Let us denote the 6 ohm , 14 ohm & 10 ohm resistors as r1, r2 & r3 respectively.

Also, the resistor of 20 ohm in middle & the resistor of 20 ohm between P & Q be r4 & r5 respectively.

We know,

For series :

Equivalent resistance = R1 + R2 + ........

For Parallel :

1/(Equivalent resistance)= 1/R1 + 1/R2 + .......

We also knew,

For same resistance (in parallel) :

Equivalent resistence= resistance/n

[ n = No of resistors ]

Therefore,

r1 & r2 are in series,

T1 = r1+ r2 = 6+14=20 ohm

T1 & r4 are in parallel,

T2 = 20/n = 20/2 = 10 ohm

T2 & r3 are in series,

T3 = T2 + r3 = 10+10= 20 ohm

Again T3 & r5 are in parallel,

T4 = 20/n = 20/2 = 10 ohm.

So, the effective resistance between P and Q is 10 ohm.

Total resistance in the circuit :

Now, 25 ohm resistor & T4 are in series.

25+10= 35 ohm

Total current in circuit = V/R = 70/35 = 2A.

We knew,

In a series circuit, current is same everywhere. So, current across 25 ohm resistor is 2A.