Question

Each of the resistors shown in fig. has resistance R. Find the equivalent resistance between A and B.


A) $\dfrac{{7R}}{4}$
B) $\dfrac{{5R}}{4}$
C) $\dfrac{{9R}}{4}$
D) $\dfrac{{11R}}{4}$

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.
All the resistance in the circuit is R. Apply the equivalent resistance to all the parallel connections. The circuit diagram will become,

The three $\dfrac{R}{2}$in the above and below of AB are in series. Both of them will be $\dfrac{{3R}}{2}$. The circuit diagram will be

The equivalent resistance between A and B is
\({R_{AB}} = R + \left(\frac{1}{\frac{3R}{2}}+\frac{1}{\frac{3R}{2}}\right)^{-1}+R\)
\({R_{AB}} = R + \frac{{3R}}{4} + R\)
\({R_{AB}} = \frac{{11}}{4}R\)

Hence, the correct option is Option (D).

Additional Information:
Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance blocks the flow of current. The S.I unit of resistance is ohms. The current decreases as resistance increases. On the other hand, the current increases as the resistance decreases.
When electrons move through a conductor, like a metal wire, an electric current occurs. The ions in the metal can collide with the traveling electrons. Resistance is created as a result and makes it more difficult for the current to flow.


Note: A component created to produce resistance is called a resistor. Resistors can be used to divide voltage, limit current, or produce heat. While solving this question pay close attention to circuits and terminals in which these resistances are connected and apply the concepts of parallel combination and series combination of resistance accordingly.