A wire with a resistance of 0.5 , Omega , m^{ | vedclass

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

Question

(C) The circumference of the circle is $2\pi R$. Given $R = 1 \, m$,the total length is $2\pi \, m$. The resistance per unit length is $0.5 \, \Omega

Vedclass · Accepted Answer

$\frac{2\pi}{\pi + 4} \, \Omega$

Vedclass · Answer

(C) The circumference of the circle is $2\pi R$. Given $R = 1 \, m$,the total length is $2\pi \, m$. The resistance per unit length is $0.5 \, \Omega \, m^{-1}$.The circle is divided into two semicircles by the diameter. The length of each semicircle is $\pi R = \pi \, m$. The resistance of each semicircle is $R_1 = R_2 = (0.5 \, \Omega \, m^{-1}) 	imes (\pi \, m) = 0.5\pi \, \Omega$.The diameter has a length equal to $2R = 2 \, m$. The resistance of the wire along the diameter is $R_3 = (0.5 \, \Omega \, m^{-1}) 	imes (2 \, m) = 1 \, \Omega$.These three resistances $(R_1, R_2, R_3)$ are connected in parallel between the two ends of the diameter ($A$ and $B$).The equivalent resistance $R_{eq}$ is given by:$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} = \frac{1}{0.5\pi} + \frac{1}{0.5\pi} + \frac{1}{1} = \frac{2}{0.5\pi} + 1 = \frac{4}{\pi} + 1 = \frac{4 + \pi}{\pi}$.Therefore,$R_{eq} = \frac{\pi}{\pi + 4} \, \Omega$. Note: The provided options in the source were slightly inconsistent; based on the calculation,the correct value is $\frac{\pi}{\pi + 4} \, \Omega$.

$A$ wire with a resistance of $0.5 \, \Omega \, m^{-1}$ is bent into a circle of radius $1 \, m$. $A$ similar wire is connected across its diameter. What is the equivalent resistance between the two ends of the diameter?

Similar Questions

$A$ ring is made of a wire having a resistance $R_0 = 12\,\Omega$. Find the ratio of the lengths $\frac{l_1}{l_2}$ of the two arcs between points $A$ and $B$ as shown in the figure,such that the equivalent resistance $R$ of the sub-circuit between these points is equal to $\frac{8}{3}\,\Omega$.

If the resistivity of all four wires connected in parallel is different as shown in the figure,and all other dimensions of the wires are the same,then the total current $i$ is (the resistance of a wire having resistivity $\rho$ is $R_0$):

The resistance of the series combination of two identical resistors is $S$. When they are joined in parallel,the total resistance is $P$. If $S = nP$,then the minimum possible value of $n$ is

$A$ uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series,the effective resistance of all the pieces is

$A$ and $B$ are two points on a uniform ring of radius $r$. The resistance of the ring is $R$. $\angle AOB = \theta$ as shown in the figure. The equivalent resistance between points $A$ and $B$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module