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
NEET
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
Two wires $A$ and $B$ of same material and mass have their lengths in the ratio $1 : 2$. On connecting them to the same source, the rate of heat dissipation in $B$ is found to be $5\,W$. The rate of heat dissipation in $A$ is............ $W$
View Solution
2
$(1)$ The product of a volt and a coulomb is a joule.

$(2)$ The product of a volt and an ampere is a joule/second.

$(3)$ The product of volt and watt is horse power.

$(4)$ Watt-hour can be measured in terms of electron volt.

State if
View Solution
3
In a meter bridge the point $D$ is neutral point as shown in the figure.
View Solution
4
A potentiometer has uniform potential gradient. The specific resistance of the material of the potentiometer wire is $10^{-7} \, ohm-meter$ and the current passing through it is $0.1\, ampere$; cross-section of the wire is $10^{-6}\, m^2$. The potential gradient along the potentiometer wire is
View Solution
5
In the circuit shown, $A$ and $V$ are ideal ammeter and voltmeter respectively. Reading of the voltmeter will be ............... $V$
View Solution
6
Two resistances of $400$ $\Omega$ and $800$ $\Omega$ are connected in series with $6\, volt$ battery of negligible internal resistance. A voltmeter of resistance $10,000$ $\Omega$ is used to measure the potential difference across $400$ $\Omega$. The error in the measurement of potential difference in volts approximately is
View Solution
7
Temperature coefficient at $0\,^oC$ is $0.00125\,^oC^{-1}$. At a temperature of $25\,^oC$ its resistance is $1\,\Omega $. Find the temperature at which resistance is $1.2\,\Omega $
View Solution
8
Which of the following statement is false
View Solution
9
Coefficient of linear expansion of material of resistor is $\alpha$. Its temperature coefficient of resistivity and resistance are $\alpha_\rho$ and $\alpha_R$ respectively, then correct relation is
View Solution
10
There are $8$ equal resistances $R$. Two are connected in parallel, such four groups are connected in series, the total resistance of the system will be
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free