An electric kettle has two heating coils. Whe | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $Q$ be the heat required to boil the water. The heat produced by a coil is given by $Q = \frac{V^2}{R} 	imes t$,where $V$ is the voltage,$R$

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) Let $Q$ be the heat required to boil the water. The heat produced by a coil is given by $Q = \frac{V^2}{R} 	imes t$,where $V$ is the voltage,$R$ is the resistance,and $t$ is the time.For the first coil: $Q = \frac{V^2}{R_1} 	imes t_1$,so $\frac{1}{R_1} = \frac{Q}{V^2 t_1}$.For the second coil: $Q = \frac{V^2}{R_2} 	imes t_2$,so $\frac{1}{R_2} = \frac{Q}{V^2 t_2}$.When connected in parallel,the equivalent resistance $R_{eq}$ is given by $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$.The heat equation for the parallel combination is $Q = \frac{V^2}{R_{eq}} 	imes t$,which gives $\frac{1}{R_{eq}} = \frac{Q}{V^2 t}$.Substituting these into the parallel resistance formula: $\frac{Q}{V^2 t} = \frac{Q}{V^2 t_1} + \frac{Q}{V^2 t_2}$.This simplifies to $\frac{1}{t} = \frac{1}{t_1} + \frac{1}{t_2}$.Substituting the given values $t_1 = 10$ and $t_2 = 40$: $\frac{1}{t} = \frac{1}{10} + \frac{1}{40} = \frac{4+1}{40} = \frac{5}{40} = \frac{1}{8}$.Therefore,$t = 8 \; min$.

Similar Questions

For what value of $R$ will the net resistance of the circuit be $18 \, \Omega$?

Two identical heaters rated $220\,V, 1000\,W$ are connected in series across a $220\,V$ supply. If the resistance does not change with temperature,the total power consumed by the combination is ............. $W$.

$A$ wire of resistance $R$ is bent to form a circular ring. Find the equivalent resistance between two points $X$ and $Y$ on its circumference. (The angle $XOY = \alpha$ is given.)

What is meant by parallel connection of resistors? Derive the equation for equivalent resistance in a parallel circuit.

In the given figure,switches $S_{1}$ and $S_{2}$ are initially open. What is the equivalent resistance across $a b$ when the switches $S_{1}$ and $S_{2}$ are closed? (in $\Omega$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module