Two wires of the same material have lengths i | vedclass

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

Question

(D) The resistance of a wire is given by $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$.Since the material is the same,$\rho$ is constant. Thus,$R \p

Vedclass · Accepted Answer

$8 : 1$

Vedclass · Answer

(D) The resistance of a wire is given by $R = ho \frac{l}{A} = ho \frac{l}{\pi r^2}$.Since the material is the same,$ho$ is constant. Thus,$R \propto \frac{l}{r^2}$.Given $\frac{l_1}{l_2} = \frac{1}{2}$ and $\frac{r_1}{r_2} = \frac{2}{1}$.The ratio of resistances is $\frac{R_1}{R_2} = \frac{l_1}{l_2} 	imes (\frac{r_2}{r_1})^2 = \frac{1}{2} 	imes (\frac{1}{2})^2 = \frac{1}{2} 	imes \frac{1}{4} = \frac{1}{8}$.When connected in parallel,the potential difference $V$ across both wires is the same.The heat produced is given by $H = \frac{V^2 t}{R}$,so $H \propto \frac{1}{R}$.Therefore,the ratio of heat produced is $\frac{H_1}{H_2} = \frac{R_2}{R_1} = \frac{8}{1}$.

Two wires of the same material have lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. If they are connected in parallel to a battery,what is the ratio of heat produced in them?

Similar Questions

In the given network, the potential difference between the points $B$ and $D$ is

Three identical bulbs are connected as shown in the figure. When switch $S$ is closed,the power consumed in bulb $B$ is $P$. What will be the power consumed by the same bulb when switch $S$ is opened?

Two resistors of $6\,\Omega$ and $9\,\Omega$ are connected in series to a $120\,V$ source. The power consumed by the $6\,\Omega$ resistor is ........... $W$.

$A$ storage battery has an $e.m.f.$ of $15\, V$ and an internal resistance of $0.05\, \Omega$. Its terminal voltage when it is delivering $10\, A$ of current is ............... $V$.

Two cells of $e.m.f.$ $E_1$ and $E_2$ and of negligible internal resistances are connected with two variable resistors as shown in the figure. When the galvanometer shows no deflection,the values of the resistances are $P$ and $Q$. What is the value of the ratio $E_2/E_1$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module