Two resistances r_1 and r_2 (r_1

Question

(D) When two resistors $r_1$ and $r_2$ are connected in parallel, the equivalent resistance $R$ is given by the formula: $\frac{1}{R} = \frac{1}{r_1}

Vedclass · Accepted Answer

$R < r_1$

Vedclass · Answer

(D) When two resistors $r_1$ and $r_2$ are connected in parallel, the equivalent resistance $R$ is given by the formula: $\frac{1}{R} = \frac{1}{r_1} + \frac{1}{r_2} = \frac{r_1 + r_2}{r_1 r_2}$.Therefore, $R = \frac{r_1 r_2}{r_1 + r_2}$.Given that $r_1 Since $R = \frac{r_1 r_2}{r_1 + r_2}$, we can write $R = r_1 \left( \frac{r_2}{r_1 + r_2} \right)$.Since $r_2 Thus, $R Similarly, it can be shown that $R < r_2$. Therefore, the equivalent resistance in a parallel combination is always less than the smallest individual resistance in the circuit.

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

Similar Questions

$10$ resistors,each of resistance $R$,are connected in series to a battery of $emf$ $E$ and negligible internal resistance. When those are connected in parallel to the same battery,the current is increased $n$ times. The value of $n$ is:

Three resistances of equal values are arranged in four different configurations as shown below. Power dissipation in the increasing order is

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 ............. $\Omega$.

Three identical resistances $A$,$B$,and $C$ are connected as shown in the given figure. The heat produced will be maximum in:

Find the equivalent resistance between $P$ and $Q$. (If each wire has a resistance $R$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module