Water boils in an electric kettle in 15,text{ | vedclass

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

Question

(C) The heat required to boil the water is given by $H = \frac{V^2}{R} t$,where $V$ is the supply voltage,$R$ is the resistance of the heating wire,an

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(C) The heat required to boil the water is given by $H = \frac{V^2}{R} t$,where $V$ is the supply voltage,$R$ is the resistance of the heating wire,and $t$ is the time taken.Since the supply voltage $V$ and the amount of heat $H$ required are the same in both cases,we have $H = \frac{V^2}{R_1} t_1 = \frac{V^2}{R_2} t_2$.This implies $\frac{t_1}{R_1} = \frac{t_2}{R_2}$,or $\frac{t_2}{t_1} = \frac{R_2}{R_1}$ ..... $(i)$We know that the resistance of a wire is proportional to its length,$R \propto l$,so $\frac{R_2}{R_1} = \frac{l_2}{l_1}$ ..... $(ii)$Substituting $(ii)$ into $(i)$,we get $\frac{t_2}{t_1} = \frac{l_2}{l_1}$.Given that the new length $l_2 = \frac{2}{3} l_1$,we have $\frac{l_2}{l_1} = \frac{2}{3}$.Substituting the values,$\frac{t_2}{15} = \frac{2}{3}$,which gives $t_2 = 15 	imes \frac{2}{3} = 10\,	ext{min}$.

Water boils in an electric kettle in $15\,\text{min}$ after switching on. If the length of the heating wire is decreased to $2/3$ of its initial value,then the same amount of water will boil with the same supply voltage in ............. $\text{min}$.

Similar Questions

Inside a superconducting ring,six identical resistors each of resistance $R$ are connected as shown in the figure. The equivalent resistance$(s)$:

In the circuit shown below,the resistances are given in $\Omega$ and the battery is assumed ideal with an emf equal to $3\,V$. The voltage across the resistance $R_4$ is ................. $V$.

Find the current in the loop.

$A$ current of $6\, A$ enters at corner $P$ of an equilateral triangle $PQR$ having $3$ wires of resistance $2 \,\Omega$ each and leaves by the corner $R$. The current $i_{1}$ in ampere is ........ .

In the circuit shown below,the current that flows from $a$ to $b$ when the switch $S$ is closed is ............... $A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module