Three unequal resistors in parallel are equiv | vedclass

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

Question

(B) Let the three resistances be $R_1, R_2$ and $R_3$. Given that $\frac{R_1}{R_2} = \frac{1}{2}$,we can write $R_1 = k$ and $R_2 = 2k$. For resistors

Vedclass · Accepted Answer

$(b)$ $6$

Vedclass · Answer

(B) Let the three resistances be $R_1, R_2$ and $R_3$. Given that $\frac{R_1}{R_2} = \frac{1}{2}$,we can write $R_1 = k$ and $R_2 = 2k$. For resistors in parallel,the equivalent resistance $R_{eq}$ is given by $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$. Substituting the given values,$\frac{1}{1} = \frac{1}{k} + \frac{1}{2k} + \frac{1}{R_3}$. Rearranging for $R_3$,we get $\frac{1}{R_3} = 1 - (\frac{1}{k} + \frac{1}{2k}) = 1 - \frac{3}{2k} = \frac{2k-3}{2k}$. Thus,$R_3 = \frac{2k}{2k-3}$. Since $R_3$ must be a positive integer and all resistors must be unequal: If $k=1$,$R_3 = -2$ (impossible). If $k=2$,$R_1=2, R_2=4, R_3=4$ (not unequal). If $k=3$,$R_1=3, R_2=6, R_3=\frac{6}{3} = 2$. Here,$R_1=3, R_2=6, R_3=2$. All are unequal and integers. The largest resistance is $6 \ \Omega$.

Three unequal resistors in parallel are equivalent to a resistance $1 \ \Omega$. If two of them are in the ratio $1:2$ and if no resistance value is fractional,then the largest of the three resistances in ohms is

Similar Questions

Four $4 \Omega$ resistors are connected together along the edges of a square. $A$ $12 \text{ V}$ battery with an internal resistance of $2 \Omega$ is connected across a pair of the diagonally opposite corners of the square. The power dissipated in the circuit is (in $\text{ W}$)

The figure shows three resistor configurations $R_1, R_2$, and $R_3$ connected to a $3 \text{ V}$ battery. If the power dissipated by the configurations $R_1, R_2$, and $R_3$ is $P_1, P_2$, and $P_3$ respectively, then:

$A$ letter $A$ is constructed of a uniform wire with resistance $1.0\,\Omega/cm$. The sides of the letter are $20\,cm$ and the cross-piece in the middle is $10\,cm$ long. The apex angle is $60^\circ$. The resistance between the ends $A$ and $D$ is ............. $\Omega$.

$A$ uniform wire of resistance $4 \ \Omega$ is bent into the shape of a semicircle. What is the equivalent resistance between the two ends of the diameter (in $\Omega$)?

In the given circuit,if all resistors have the same value $R$,then the maximum equivalent resistance will be between which points?

Vedclass Test Series

Exam Paper Generator

Online Exam Module