Three identical resistors R_1 = R_2 = R_3 = R | vedclass

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

Question

(B) Let the resistance of each resistor be $R$. In the given circuit,$R_2$ and $R_3$ are connected in parallel. Their equivalent resistance is $R_p =

Vedclass · Accepted Answer

Greatest in $R_1$

Vedclass · Answer

(B) Let the resistance of each resistor be $R$. In the given circuit,$R_2$ and $R_3$ are connected in parallel. Their equivalent resistance is $R_p = \frac{R 	imes R}{R + R} = \frac{R}{2}$. This parallel combination is in series with $R_1$. The total resistance of the circuit is $R_{eq} = R_1 + R_p = R + \frac{R}{2} = \frac{3R}{2}$. The total current flowing through the circuit is $I = \frac{V}{R_{eq}} = \frac{V}{3R/2} = \frac{2V}{3R}$. This entire current $I$ flows through $R_1$. Thus,the power dissipated in $R_1$ is $P_1 = I^2 R = (\frac{2V}{3R})^2 R = \frac{4V^2}{9R}$. The current $I$ splits equally between $R_2$ and $R_3$ because they are identical. So,the current through $R_2$ (and $R_3$) is $I_2 = I_3 = \frac{I}{2} = \frac{V}{3R}$. The power dissipated in $R_2$ is $P_2 = I_2^2 R = (\frac{V}{3R})^2 R = \frac{V^2}{9R}$. Comparing the powers,$P_1 = \frac{4V^2}{9R}$ and $P_2 = P_3 = \frac{V^2}{9R}$. Clearly,$P_1 > P_2 = P_3$. Therefore,the power dissipated is greatest in $R_1$.

Three identical resistors $R_1 = R_2 = R_3 = R$ are connected as shown to a battery of constant e.m.f. $V$. The power dissipated is:

Similar Questions

For three resistors of different values connected in series,obtain the equation for equivalent resistance. From this,write the equation for $n$ resistors connected in series.

Four wires of equal length and of resistances $10 \ \Omega$ each are connected in the form of a square. The equivalent resistance between two opposite corners of the square is ............. $\Omega$. (in $\Omega$)

Three conductors draw currents of $1 \,A, 2 \,A$ and $3 \,A$ respectively, when connected in turn across a battery. If they are connected in series and the combination is connected across the same battery, the current drawn will be

The equivalent resistance across points $A$ and $B$ in the circuit shown below is:

Twelve resistors each of resistance $16 \,\Omega$ are connected in the circuit as shown. The net resistance between $A$ and $B$ (any two conjugate points of the outer square) is ............... $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module