Two coils require 20 min and 60 min respect | vedclass

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

Question

(B) The heat energy produced is given by $H = \frac{V^2}{R} t$. Since the heat produced $H$ and the voltage $V$ are the same for both cases,we have $H

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(B) The heat energy produced is given by $H = \frac{V^2}{R} t$. Since the heat produced $H$ and the voltage $V$ are the same for both cases,we have $H = \frac{V^2}{R_1} t_1 = \frac{V^2}{R_2} t_2$.Given $t_1 = 20 \ min$ and $t_2 = 60 \ min$,we get $\frac{20}{R_1} = \frac{60}{R_2}$,which implies $R_2 = 3R_1$.When connected in parallel,the equivalent resistance $R_{eq}$ is given by $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_1} + \frac{1}{3R_1} = \frac{4}{3R_1}$.Thus,$R_{eq} = \frac{3R_1}{4}$.For the same heat $H$ to be produced by the parallel combination in time $t$,we have $H = \frac{V^2}{R_{eq}} t$.Equating this to the heat produced by the first coil: $\frac{V^2}{R_1} 	imes 20 = \frac{V^2}{(3R_1/4)} 	imes t$.$20 = \frac{4}{3} t \Rightarrow t = \frac{20 	imes 3}{4} = 15 \ min$.

Similar Questions

In a series $LR$ circuit,$X_L = 3R$. Now,a capacitor with $X_C = R$ is added in series. What is the ratio of the new power factor to the old power factor?

Consider the parallel $LCR$ circuit shown in the figure. Find the net current $i$ and the phase of $i$. Show that $i = \frac{V}{Z}$. Find the impedance $Z$ for this circuit.

In the given $LCR$ $AC$ circuit,the effective current flowing through the circuit will be:

With a gradual increase in the frequency of an $A.C.$ supply, the impedance of an $LCR$ series circuit

Vedclass Test Series

Exam Paper Generator

Online Exam Module