
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
164.4k+ views
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.
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.
Recently Updated Pages
Environmental Chemistry Chapter for JEE Main Chemistry

Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Degree of Dissociation and Its Formula With Solved Example for JEE

Wheatstone Bridge for JEE Main Physics 2025

Instantaneous Velocity - Formula based Examples for JEE
