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. 

Answer 1

(i) Resistance are connected in series :

`therefore` V = V₁ + V₂ + V₃ 

Same current will pass through all resistors 

Using ohm's law , 

`therefore` IR_s = IR₁ + IR₂ + IR₃ 

`therefore`  IR_s = I (R₁ + R₂ + R₃)

`therefore` R_s = R₁ + R₂ + R₃ 

where , R_s → 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` .