Question

In the network shown below, the ring has zero resistance. The equivalent resistance between the point A and B is

A) 2R
B) 4R
C) 7R
D) 10R

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.
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.
Here, in this case, the ring has zero resistance and the three $3R$resistances are in parallel connection. So the equivalent resistance will be.
$\dfrac{1}{{{R_E}}} = \dfrac{1}{{3R}} + \dfrac{1}{{3R}} + \dfrac{1}{{3R}} = \dfrac{1}{R}$
\[{R_E} = R\]
Then between points A and B, the two resistances \[{R_E}\]and \[R\]are in series combination.
Then equivalent resistance between A and B = \[R + R = 2R\]

Hence, the correct option is Option (A) 2R.

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 travelling electrons. Resistance is created as a result and makes it more difficult for the current to flow.



Note: A device created to produce resistance is called a resistor. Resistors can be used to divide voltage, limit current, or produce heat. Fixed and variable resistors are the two main types of resistors. In other words, a resistor is a passive two-terminal electrical component used in circuits to implement electrical resistance.