Question

Judge the equivalent resistance when the following are connected in parallel : (i) 1 Ω and 106 Ω, (if) 1 Ω and 103 Ω and 106 Ω.​

Answer 1

Answer:

I) Given that 1 Ω and 106 Ω are connected in parallel then the equivalent resistance R will be

1/R = 1/1 + 1/ 106

= 106 + 1 / 106

= 1

R = 1 Ω

Equivalent resistance is 1 Ω

ii) 1 Ω and 103Ω and 106Ω are in parallel

1/R = 1/1 + 1/103 + 1/ 106

=106 + 1 + 10 3/ 106

R = 0.999 Ω

Therefore, equivalent resistance = 0.999 Ω

Answer 2

Since 1/R=1/R1+1/R2+1/R3+..+1/Rn

when resistors are connected in parallel

(a) 1 Ω and 106 Ω

Thus, 1/R=1/1Ω+1/106Ω=106+1/106Ω=107/106Ω

Thus, R=106/107Ω=0.99Ω

Thus, equivalent resistance of 1Ω and 106Ω are connected in parallel = 0.99Ω

(b)  1 Ω and 103 Ω, and 106 Ω

Thus, 1/R=1/1Ω+1/103Ω+1/106Ω=(10918+106+103)/103×106Ω=11127/10918Ω

Thus, R=10918/11127Ω=1.02Ω

Thus, equivalent resistance of  1 Ω, 103 Ω and 106 Ω are connected in parallel = 1.02Ω