Question

The equivalent resistance between points A and B is

A) 2R
B) (3/4) R
C) (4/3) R
D) (3/5) R

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.
Let’s redraw the circuit diagram for simplicity.

Figure 1
The equivalent resistance for the parallel resistance connection is
$\dfrac{1}{{{R_E}}} = \dfrac{1}{R} + \dfrac{1}{R} = \dfrac{2}{R} \Rightarrow {R_E} = \dfrac{R}{2}$
The circuit diagram will be

Figure 2
The equivalent resistance for the series resistance connection is
${R_E} = \dfrac{R}{2} + R = \dfrac{3}{2}R$
Now the circuit diagram will be

Figure 3
Now the equivalent resistance for the final parallel resistance connection is
${R_{AB}} = \dfrac{{\dfrac{3}{2}R \times R}}{{\dfrac{3}{2}R + R}}$
${R_{AB}} = \dfrac{3}{2}{R^2} \times \dfrac{2}{{5R}} = \dfrac{3}{5}R$

Hence, the correct option is Option (D).



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.