Question

Find the equivalent resistance between (1) points
A and B, (ii) point Cand D in the following
network.​

Answer 1

Explanation:

Solution

(i) The resistors 3Ω3Ω and 7Ω7Ω are in series. Their total resistance = 3+7=10Ω3+7=10Ω.

This resistance is in parallel with 10Ω10Ω. The effective resistance between A and C =10×1010+10=5Ω=10×1010+10=5Ω

This resistance is in series with resistance 5Ω5Ω, the effective resistance =5+5=10Ω=5+5=10Ω

This resistance is in parallel with resistor 10Ω10Ω in arm AB. Thus equivalent resistance between A and B = 10×1010+10=5Ω10×1010+10=5Ω

(ii) The resistance of arm ABC (=5+10=15Ω=5+10=15Ω) is in parallel with resistance 10Ω10Ω of arm AC.

Thier effective resistance= 15×1515+10=6Ω15×1515+10=6Ω

This resistance is in series wiht resistance 7Ω7Ω of arm CD. Their effective resistance =6+7=13Ω=6+7=13Ω. This resistance is in parallel with resistance 3Ω3Ω of arm AD.

The equivalent resistance between An and D

13×1313+3=3916Ω13×1313+3=3916Ω

(iii) The resistance of arm ADC = 3+7=10Ω3+7=10Ω

Resistance of arm ABC =10+5=15Ω=10+5=15Ω

These resistance are in parallel.

They are also in parallel with resistance 10Ω10Ω of arm AC.

Therefore, equivalent resistance between A and C is

1Req=110+110+115=8301Req=110+110+115=830 or Req=308=154ΩReq=308=154Ω