Two heaters take 10 minutes and 20 minutes re | vedclass

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

Question

(B) The heat required to raise the temperature of a given mass of water is $H = \frac{V^2}{R} t$. Since $H$ and $V$ are the same for both heaters,we h

Vedclass · Accepted Answer

$\frac{20}{3}$ minutes

Vedclass · Answer

(B) The heat required to raise the temperature of a given mass of water is $H = \frac{V^2}{R} t$. Since $H$ and $V$ are the same for both heaters,we have $t \propto R$. Let $R_1$ and $R_2$ be the resistances of the two heaters. Then $R_1 \propto t_1 = 10$ and $R_2 \propto t_2 = 20$. When connected in parallel,the equivalent resistance $R_{	ext{eq}}$ is given by $\frac{1}{R_{	ext{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{R_1 + R_2}{R_1 R_2}$,so $R_{	ext{eq}} = \frac{R_1 R_2}{R_1 + R_2}$. Since $t \propto R$,the equivalent time $t_{	ext{eq}}$ is $t_{	ext{eq}} = \frac{t_1 t_2}{t_1 + t_2}$. Substituting the given values: $t_{	ext{eq}} = \frac{10 	imes 20}{10 + 20} = \frac{200}{30} = \frac{20}{3}$ minutes.

Two heaters take $10$ minutes and $20$ minutes respectively to heat the same amount of water. If the heaters are connected in parallel,what would be the time required to heat the same amount of water?

Similar Questions

What is the maximum voltage that can be safely applied across a resistor of $196 \,\Omega - 1 \,W$ rating? .......... $volt$

The resistance of a bulb filament changes with temperature. If a bulb rated at $220 \ V$ and $100 \ W$ is connected to a supply of $(220 \times 0.8) \ V$,the actual power consumed will be:

The emf of a car battery is $12 \ V$. If the internal resistance of the battery is $0.4 \ \Omega$,then the maximum power drawn from the battery is . . . . . . $W$.

$A$ resistor develops $300 \,J$ of thermal energy in $15 \,s$,when a current of $2 \,A$ is passed through it. If the current increases to $3 \,A$,the energy developed in $10 \,s$ is........$J.$

Two electric bulbs $A$ and $B$ are rated as $60\, W$ and $100\, W$. They are connected in parallel to the same source. Then,

Vedclass Test Series

Exam Paper Generator

Online Exam Module