Two wires 'A' and 'B' of the same material have their lengths in the ratio 1 : 2 and radii in the ratio 2 :

Q: Two wires '$A$' and '$B$' of the same material have their lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. The two wires are connected in parallel across a battery. The ratio of the heat produced in '$A$' to the heat produced in '$B$' for the same time is

d (d) ${R_1} = \rho \frac{{{l_1}}}{{{A_1}}}$ and ${R_2} = \rho \frac{{{l_2}}}{{{A_2}}}$$ \Rightarrow $$\,\frac{{{R_1}}}{{{R_2}}} = \frac{{{l_1}}}{{{l_2}}}.\frac{{{A_2}}}{{{A_1}}} = \frac{{{l_1}}}{{{l_2}}}{\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2}$ Given $\frac{{{l_1}}}{{{l_2}}} = \frac{1}{2}$ and $\frac{{{r_1}}}{{{r_2}}} = \frac{2}{1}$ or $\frac{{{r_2}}}{{{r_1}}} = \frac{1}{2}$$ \Rightarrow $ $\frac{{{R_1}}}{{{R_2}}} = \frac{1}{8}$ $\therefore $ Ratio of heats $\frac{{{H_1}}}{{{H_2}}} = \frac{{{V^2}/{R_1}}}{{{V^2}/{R_2}}} = \frac{{{R_2}}}{{{R_1}}} = \frac{8}{1}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

Two wires '$A$' and '$B$' of the same material have their lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. The two wires are connected in parallel across a battery. The ratio of the heat produced in '$A$' to the heat produced in '$B$' for the same time is

A$1:2$
B$2:1$
C$1:8$
D$8:1$

Medium

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
A conducting wire of length $ l$ area of cross-section $A$ and electric resistivity $\rho$ is connected between the terminals of a battery. $A$ potential difference $V$ is developed between its ends, causing an electric current.If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be
View Solution
2
Resistance of tungsten wire at $150\,^oC$ is $133\,\Omega $. Its resistance temperature coefficient is $0.0045\,^oC$. The resistance of this wire at $500\,^oC$ will be .............. $\Omega$
View Solution
3
A potentiometer circuit shown in the figure is set up to measure $e.m.f.$ of a cell $E$. As the point $P$ moves from $X$ to $Y$ the galvanometer $G$ shows deflection always in one direction, but the deflection decreases continuously until $Y$ is reached. In order to obtain balance point between $X$ and $Y$ it is necessary to
View Solution
4
A platinum resistance thermometer has a resistance of $50\,\Omega $ at $20\,^o C$. When dipped in a liquid the resistance becomes $76.8\,\Omega $. The temperature coefficient of resistance for platinum is $\alpha = 3.92 \times {10^{ - 3}}\,^o C$. The temperature of the liquid is .............. $^o C$
View Solution
5
The potential difference across the $100\,\Omega$ resistance in the following circuit is measured by a voltmeter of $900 \,\Omega$ resistance. The percentage error made in reading the potential difference is
View Solution
6
Which of the following statement is correct
View Solution
7
Calculate equivalent resistance across $A-B$ ............... $\Omega$
View Solution
8
Infinite number of cells having $emf$ and internal resistance $\left( {E,r} \right)$, $\left( {\frac{E}{n},\frac{r}{n}} \right)$, $\left( {\frac{E}{{{n^2}}},\frac{r}{{{n^2}}}} \right)$, $\left( {\frac{E}{{{n^3}}},\frac{r}{{{n^3}}}} \right)$..... are connected in series in same manner across an external resistance of $\frac{{nr}}{{n + 1}}$ . Current flowing through the external resistor is
View Solution
9
Dimensions of a block are $1\,cm \times 1\,cm \times 100\,cm$. If specific resistance of its material is $3 \times {10^{ - 7}}\,ohm - m$, the resistance between the square faces is
View Solution
10
Equivalent resistance between $A$ and $B$ will be ............ $ohm$
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free