A wire of resistance 9 Omega is bent to form | vedclass

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

Question

(C) The total resistance of the wire is $9 \ \Omega$. Since it is bent into an equilateral triangle,the wire is divided into three equal parts,each ha

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) The total resistance of the wire is $9 \ \Omega$. Since it is bent into an equilateral triangle,the wire is divided into three equal parts,each having a resistance of $R' = 9 \ \Omega / 3 = 3 \ \Omega$.When we consider the equivalent resistance across any two vertices (say $B$ and $C$),the resistor between $B$ and $C$ is in parallel with the series combination of the other two resistors (between $A-B$ and $A-C$).The resistance of the branch $AB$ and $AC$ in series is $R_{series} = 3 \ \Omega + 3 \ \Omega = 6 \ \Omega$.Now,this $6 \ \Omega$ resistance is in parallel with the $3 \ \Omega$ resistor connected directly between $B$ and $C$.The equivalent resistance $R_{eq}$ is given by:$\frac{1}{R_{eq}} = \frac{1}{6} + \frac{1}{3} = \frac{1+2}{6} = \frac{3}{6} = \frac{1}{2}$.Therefore,$R_{eq} = 2 \ \Omega$.

$A$ wire of resistance $9 \ \Omega$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be . . . . . . ohm.

Similar Questions

Find the net resistance between points $X$ and $Y$ for the given infinite ladder network,where each resistor has a resistance of $R$.

The effective resistance of a parallel connection that consists of four wires of equal length,equal area of cross-section,and same material is $0.25\, \Omega$. What will be the effective resistance if they are connected in series? (In $\Omega$)

The equivalent resistance between the points $P$ and $Q$ in the network given here is equal to ................ $\Omega$ (given $r = \frac{3}{2} \Omega$).

The resistive network shown below is connected to a $D.C.$ source of $16 \, V$. The power consumed by the network is $4 \, W$. The value of $R$ is ............. $\Omega$.

$3$ identical bulbs are connected in series and these together dissipate a power $P$. If now the bulbs are connected in parallel,then the power dissipated will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module