Water boils in an electric kettle in 15,min after switching on. If the length of the heating wire is decreased to 2/3 of its initial

Q: Water boils in an electric kettle in $15\,\min$ 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 ............. $min$

c $H = \frac{{{V^2}}}{R}t$ Since supply voltage is same and equal amount of heat will produce, therefore $\frac{{{R_1}}}{{{t_1}}} = \frac{{{R_2}}}{{{t_2}}}$ or $\frac{{{R_1}}}{{{R_2}}} = \frac{{{t_1}}}{{{t_2}}}$ ..... $(i)$ But $R \propto l$ $ \Rightarrow $ $\frac{{{R_1}}}{{{R_2}}} = \frac{{{l_1}}}{{{l_2}}}$..... $(ii)$ By $(i)$ and $(ii)$, $\frac{{{l_1}}}{{{l_2}}} = \frac{{{t_1}}}{{{t_2}}}$..... $(iii)$ Now ${l_2} = \frac{2}{3}\,\,{l_1}$ $ \Rightarrow $ $\frac{{{l_1}}}{{{l_2}}} = \frac{3}{2}$ By equation $(iii)$, $\frac{3}{2} = \frac{{15}}{{{t_2}}}$ $ \Rightarrow $ ${t_2} = 10\,\min$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

Water boils in an electric kettle in $15\,\min$ 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 ............. $min$

A$15$
B$12$
C$10$
D$8$

Diffcult

STD 11 Science
JEE
STD 12 - 3. current electricity
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
In a potentiometer experiment shown here, for the position $X$ of the jockey $J,$ there occurs a null deflection in the galvanometer. Then the potential difference between points $A$ and $X$ is ................ $V$
View Solution
2
Figure shows three similar lamps $L_1, L_2$ and $L_3$ connected across a power supply. If the lamp $L_3$ fuses, how will the light emitted by $L_1$ and $L_2$ change ?
View Solution
3
In a circuit shown in the figure, the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition, a current of $1 \mathrm{~A}$ flows through the $1 \Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement($s$) is(are) correct?

[Given: $\mathrm{e}^{-1}=0.36$ ]

($A$) The value of the resistance $R$ is $3 \Omega$.

($B$) For $t$

($C$) At $t=t_0+7.2 \mu \mathrm{s}$, the current in the capacitor is $0.6 \mathrm{~A}$.

($D$) For $t \rightarrow \infty$, the charge on the capacitor is $12 \mu C$.
View Solution
4
A wire of resistance $20 \Omega$ is divided into $10$ equal parts. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is_______.0$\Omega$.
View Solution
5
A potentiometer wire has length $4\,\, m$ and resistance $8\,\,\Omega $. The resistance that must be connected in series with the wire and an accumulator of e.m.f. $2\,\, V,$ so as to get a potential gradient $1\,\, m \,V$ per $cm$ on the wire is ............. $\Omega$
View Solution
6
If the length of the filament of a heater is reduced by $10\%$, the power of the heater will
View Solution
7
Forty electric bulbs are connected in series across a $220\, V$ supply. After one bulb is fused, the remaining $39$ are connected again in series across the same supply. The illumination will be
View Solution
8
In the figure given the value of $X$ resistance will be, when the $p.d.$ between $B$ and $D$ is zero ................... $ohm$
View Solution
9
All wires have same resistance and equivalent resistance between $A$ and $B$ is $R$. Now keys are closed, then the equivalent resistance will become
View Solution
10
A current of $5\, A$ passes through a copper conductor (resistivity $= 1.7\times10^{-8}\,\Omega \,m$) of radius of cross-section $5\, mm$. Find the mobility of the charges if their drift velocity is $1.1\times10^{-3}\, m/s$ ................ $m^2/Vs$
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free