Question

A wire when connected to 220 V mains supply has power dissipation. Now the wire is cut into
case is. Then is
two equal pieces which are connected in parallel to the same supply. Power dissipation in this
(A) 1
(B) 4
(C) 2
(D)3​

Answer 1

Correct Question :

A wire when connected to 220V mains supply has power dissipation P₁. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is P₂  . Then P₂:P₁ is

(A) 1

(B) 4

(C) 2

(D) 3

Solution :

Relation b/w Power , Voltage and Resistance is given by ,

$\bigstar\ \; \sf \pink{P=\dfrac{V^2}{R}}$

Initial power having resistance R is ,

$\sf P_1=\dfrac{V^2}{R_1}\\\\:\implies \sf P_1=\dfrac{(220)^2}{R}...(1)$

Now the wire is cut into two equal pieces which are connected in parallel to the same supply of voltage .

$\sf \dfrac{1}{R_{p}}=\dfrac{1}{R/2}+\dfrac{1}{R/2}\\\\:\implies \sf \dfrac{1}{R_p}=\dfrac{2}{R}+\dfrac{2}{R}\\\\:\implies \sf \dfrac{1}{R_p}=\dfrac{4}{R}\\\\:\implies \sf \green{R_p=\dfrac{R}{4}}\ \; \bigstar$

Power 2  ( P₂ ) ,

$\sf P_2=\dfrac{V^2}{R_p}$

$:\implies \sf P_2=\dfrac{(220)^2}{\frac{R}{4}}\\\\:\implies \sf P_2=4\left(\dfrac{(220)^2}{R}\right)\\\\:\implies \sf P_2=4P_1$

So , P₂ : P₁

⇒ 4P₁ : P₁

⇒ 4 : 1

⇒  4  $\purple{\bigstar}$

Option (B) is correct