If the ratio of the equivalent resistance of | vedclass

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

Question

(D) The equivalent resistance in series is $R_S = R_1 + R_2$.The equivalent resistance in parallel is $R_P = \frac{R_1 R_2}{R_1 + R_2}$.Given the rati

Vedclass · Accepted Answer

${\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^{1/2}} + {\left( {\frac{{{R_2}}}{{{R_1}}}} \right)^{1/2}} = {n^{1/2}}$

Vedclass · Answer

(D) The equivalent resistance in series is $R_S = R_1 + R_2$.The equivalent resistance in parallel is $R_P = \frac{R_1 R_2}{R_1 + R_2}$.Given the ratio $\frac{R_S}{R_P} = n$,we have:$\frac{R_1 + R_2}{\frac{R_1 R_2}{R_1 + R_2}} = n$This simplifies to:$\frac{(R_1 + R_2)^2}{R_1 R_2} = n$Taking the square root on both sides:$\frac{R_1 + R_2}{\sqrt{R_1 R_2}} = \sqrt{n}$Dividing each term in the numerator by the denominator:$\frac{R_1}{\sqrt{R_1 R_2}} + \frac{R_2}{\sqrt{R_1 R_2}} = \sqrt{n}$This results in:$\sqrt{\frac{R_1}{R_2}} + \sqrt{\frac{R_2}{R_1}} = \sqrt{n}$Which can be written as:${\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^{1/2}} + {\left( {\frac{{{R_2}}}{{{R_1}}}} \right)^{1/2}} = {n^{1/2}}$.

If the ratio of the equivalent resistance of two resistors $R_1$ and $R_2$ in series to that in parallel is $n$,then:

Similar Questions

$A$ current of $3 \, A$ flows through the $2 \, \Omega$ resistor shown in the circuit. The power dissipated in the $5 \, \Omega$ resistor is ................. $W$.

Two resistances $r_1$ and $r_2$ $(r_1 < r_2)$ are joined in parallel. The equivalent resistance $R$ is such that

$A$ wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is ( $E$ is the mid-point of arm $CD$ ).

$A$ ring is made of a wire having a resistance $R_0 = 12 \,\Omega$. Find the points $A$ and $B$,as shown in the figure,at which a current-carrying conductor should be connected so that the resistance $R$ of the sub-circuit between these points is equal to $\frac{8}{3} \,\Omega$.

In the given circuit,all resistances are of value $R \ \Omega$ each. The equivalent resistance between $A$ and $B$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module