Two wires A and B made of the same material a | vedclass

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

Question

(B) Since the wires are connected in series,the current $I$ flowing through both wires is the same.Using Ohm's law,$V = IR$,so $V \propto R$.Given $\f

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(B) Since the wires are connected in series,the current $I$ flowing through both wires is the same.Using Ohm's law,$V = IR$,so $V \propto R$.Given $\frac{V_A}{V_B} = \frac{3}{2}$ and $\frac{L_A}{L_B} = \frac{6}{1}$.The resistance $R$ is given by $R = ho \frac{L}{A} = ho \frac{L}{\pi r^2}$.Since the material is the same,$ho$ is constant,so $R \propto \frac{L}{r^2}$.Therefore,$\frac{V_A}{V_B} = \frac{R_A}{R_B} = \frac{L_A}{r_A^2} 	imes \frac{r_B^2}{L_B}$.Substituting the values: $\frac{3}{2} = \frac{6}{1} 	imes \left( \frac{r_B}{r_A} ight)^2$.$\left( \frac{r_B}{r_A} ight)^2 = \frac{3}{2} 	imes \frac{1}{6} = \frac{3}{12} = \frac{1}{4}$.Taking the square root,$\frac{r_B}{r_A} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.

Two wires $A$ and $B$ made of the same material and having their lengths in the ratio $6 : 1$ are connected in series. The potential differences across the wires are $3\,V$ and $2\,V$ respectively. If $r_A$ and $r_B$ are the radii of $A$ and $B$ respectively,then $\frac{r_B}{r_A}$ is

Similar Questions

The power of an electric motor is $242 \ W$ when connected to a $220 \ V$ supply. When the motor is operated at $200 \ V$,the current drawn by it is (in $A$)

$A$ filament bulb $(500 \,W, 100 \,V)$ is to be used in a $230 \,V$ main supply. When a resistance $R$ is connected in series,it works perfectly and the bulb consumes $500 \,W$. The value of $R$ is .................. $\Omega$.

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?

In the given circuit,what is the voltage between $P$ and $Q$ in $V$?

The potential difference across the $8\ \Omega$ resistance is $48\ V$ as shown in the figure. The value of the potential difference across points $X$ and $Y$ will be ............... $V$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module