Question

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

A) P and R
B) P and Q
C) Q and R
D) Any two points

Answer 1

Hint:The problem is from the electricity part of physics. We can apply the concept of parallel combination and series combination of resistance here. Use the equation for effective resistance in parallel and series combinations.


Formula Used:
Equivalent resistance for a series resistance circuit:
${R_E} = {R_1} + {R_2} + {R_3}$
Where ${R_E}$= equivalent resistance and ${R_1},{R_2},{R_3}$ = component resistance.
Equivalent resistance for a parallel resistance circuit:
$\dfrac{1}{{{R_E}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$
Where ${R_E}$= equivalent resistance and ${R_1},{R_2},{R_3}$ = component resistance.



Complete answer:
The equivalent resistance is a single resistance which can replace all the component resistances in a circuit in such a manner that the current in the circuit remains unchanged.
The net resistance in PR:
$\dfrac{1}{{{R_{PR}}}} = \dfrac{1}{r} + \dfrac{1}{r} + \dfrac{1}{r} \Rightarrow {R_{PR}} = \dfrac{3}{r}$
The net resistance in QR:
$\dfrac{1}{{{R_{QR}}}} = \dfrac{1}{r} + \dfrac{1}{r} \Rightarrow {R_{QR}} = \dfrac{2}{r}$
The net resistance in PQ:
${R_{PQ}} = r$
So, the net resistance is maximum between P and Q

Hence, the correct option is Option (B).



Note: Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance blocks the flow of current. The current decreases as resistance increases. On the other hand, the current increases as the resistance decreases. In short circuit conditions the current through the circuit increases exponentially because resistance of the circuit becomes zero.