Six equal resistances are connected between p | vedclass

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

Question

(B) Let each resistance be $r$. The circuit consists of three branches between the nodes $P, Q,$ and $R$.Branch $PQ$ has one resistance $r$.Branch $QR

Vedclass · Accepted Answer

$P$ and $Q$

Vedclass · Answer

(B) Let each resistance be $r$. The circuit consists of three branches between the nodes $P, Q,$ and $R$.Branch $PQ$ has one resistance $r$.Branch $QR$ has two resistances in parallel,so its equivalent resistance is $r_{QR} = r/2$.Branch $PR$ has two resistances in parallel,so its equivalent resistance is $r_{PR} = r/2$.$1$. Resistance between $P$ and $Q$ $(R_{PQ})$:$R_{PQ}$ is the parallel combination of the branch $PQ$ (resistance $r$) and the series combination of branches $PR$ and $QR$ (resistance $r/2 + r/2 = r$).$R_{PQ} = \frac{r 	imes r}{r + r} = \frac{r}{2} = 0.5r$.$2$. Resistance between $Q$ and $R$ $(R_{QR})$:$R_{QR}$ is the parallel combination of the branch $QR$ (resistance $r/2$) and the series combination of branches $PQ$ and $PR$ (resistance $r + r/2 = 1.5r$).$R_{QR} = \frac{(r/2) 	imes (1.5r)}{(r/2) + (1.5r)} = \frac{0.75r^2}{2r} = 0.375r$.$3$. Resistance between $P$ and $R$ $(R_{PR})$:$R_{PR}$ is the parallel combination of the branch $PR$ (resistance $r/2$) and the series combination of branches $PQ$ and $QR$ (resistance $r + r/2 = 1.5r$).$R_{PR} = \frac{(r/2) 	imes (1.5r)}{(r/2) + (1.5r)} = 0.375r$.Comparing the values: $R_{PQ} = 0.5r$,$R_{QR} = 0.375r$,and $R_{PR} = 0.375r$.Thus,the net resistance is maximum between $P$ and $Q$.

Six equal resistances are connected between points $P, Q$ and $R$ as shown in the figure. Then the net resistance will be maximum between:

Similar Questions

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

If the resistance between each dot is $R$,then the equivalent resistance between $A$ and $B$ is:

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

How can resistors be connected? Explain.

When two conducting wires are connected in series,the equivalent resistance is $14\, \Omega$,and when they are connected in parallel,the equivalent resistance is $3.43\, \Omega$. The resistance of the wire with the higher value is ................. $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module