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Question
Three resistors of resistances R1 , R2 and R3 are connected (i) in series, and (ii) in parallel. Write expressions for the equivalent resistance of the combination in each case.
Solution
(i) Resistance are connected in series :
`therefore` V = V1 + V2 + V3
Same current will pass through all resistors
Using ohm's law ,
`therefore` IRs = IR1 + IR2 + IR3
`therefore` IRs = I (R1 + R2 + R3)
`therefore` Rs = R1 + R2 + R3
where , Rs → Equivalent resistnace in series.
(ii) Resistors connected in parallel :
Potential difference across the resistors will be same
`therefore` I = I1 + I2 +I3
Using Ohm’s law
`therefore V/R_P = V/R_1 + V/R_2 + V/R_3`
`therefore 1/R_P = 1/R_1 + 1/R_2 + 1/R_3` .
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