Question

Obtain an expression for the effective resistance in the combination of two resistors R1 and R2 in parallel. Sketch the combination also

Answer 1

we have to obtain an expression for the effective resistance in the combination of two resistors R₁ and R₂ in parallel. have to skatch the combination also.

solution : see diagram, here two resistors of resistances R₁ and R₂ are joined in parallel with a circuit of emf V.

let i₁ is current passing through the resistor R₁ and i₂ is current passing through the resistor R₂.

we know, if resistors are joined in parallel combination, potential difference across each resistors must be same.

so, V = i₁R₁ and V = i₂R₂ [ from Ohm's law ]

let effective resistance is Req

then V = iReq

here i = i₁ + i₂

⇒V/Req = V/R₁ + V/R₂

⇒1/Req = 1/R₁ + 1/R₂, This is required expression.

Therefore effective resistance of two resistors R₁ and R₂ joined in parallel, is given by, 1/Req = 1/R₁ + 1/R₂