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Judge the equivalent resistance when the...

Judge the equivalent resistance when the following are connected in parallel:
`1 Omega,10^3 Omega and 10^6 Omega`

Text Solution

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(a) Less than 1`Omega` (but approximately `1 Omega`)
(b) less than `1 Omega` (but approximately `1 Omega`)
Explanation: When resistors are connected in parallel. the equivalent resistance is less than the least resistance (here in both the cases it is 1 `Omega`) connected in the combination.
Here, `R_1 = 1Omega, R_2 = 10^3 Omega and R_3 =10^6 Omega`
The equivalent resistance `R_p` of the parallel combination is given by,
`1/R_p = 1/R_1 + 1/R_2 +1/R_3`
`= 1/1 + 1/1000 + 1/1000000`
`= (1000000 +1000 +1)/(1000000)`
`= 1001001/(1000000)`
`:. R_p =1000000/1001001 Omega`
`~~ 1Omega`
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