Answer
417.9k+ views
Hint The configuration of the wires is similar to that of a Wheatstone bridge. The voltage between the two parallel resistors of a Wheatstone bridge is zero if it is balanced. So on removing the middle wire, we can then calculate the equivalent resistance.
In this solution we will be using the following formula;
$\Rightarrow \dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + ... + \dfrac{1}{{{R_n}}}$ where ${R_{eq}}$ is the equivalent resistance of a resistors in parallel, ${R_1}....{R_n}$ are the individual resistors in the parallel configuration.
$\Rightarrow {R_{eqs}} = {R_1} + {R_2} + ... + {R_n}$where${R_{eqs}}$ is the equivalent resistance of resistors in series and ${R_1}....{R_n}$ are the individual resistances.
Complete step by step answer
The figure above shows the wire after it has been made into a square with the sixteen ohms resistor connected across the two corners of the square. This configuration resembles a Wheatstone bridge as shown in the figure below in a more familiar setting
To calculate the equivalent resistance, we assume a voltage is applied at any of the opposite corners of the square. This is allowed because all resistances are equal.
Let’s say we placed the voltage at the opposite corners to where the 16 Ohms resistor is connected. Since, it is a balanced Wheatstone bridge, the voltage across the 16 Ohms is zero. Hence, we can ignore the 16 Ohms resistance. The two resistance at the top are in series, likewise the two at the bottom. Hence,
For top resistance
$\Rightarrow {R_{eq1}} = {R_1} + {R_2} = 4 + 4 = 8\Omega $
For bottom resistance, similarly,
$\Rightarrow {R_{eq2}} = 4 + 4 = 8\Omega $,
This two resistance are in parallel, and hence calculated as
$\Rightarrow \dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_{eq1}}}} + \dfrac{1}{{{R_{eq2}}}} = \dfrac{1}{8} + \dfrac{1}{8}$
Computing we have that
$\Rightarrow \dfrac{1}{{{R_{eq}}}} = \dfrac{1}{4}$
$\Rightarrow {R_{eq}} = 4\Omega $
Hence, the correct option is D.
Note
To avoid confusions, we are allowed to assume a voltage across the opposite corners because from the definition of equivalent resistance of a circuit, it is the one resistance to the current flow in a circuit which can replace all the resistances in the circuit. Since the voltage across 16 Ohms is zero, no current flows through the resistor, and thus does not count to the equivalent resistance.
In this solution we will be using the following formula;
$\Rightarrow \dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + ... + \dfrac{1}{{{R_n}}}$ where ${R_{eq}}$ is the equivalent resistance of a resistors in parallel, ${R_1}....{R_n}$ are the individual resistors in the parallel configuration.
$\Rightarrow {R_{eqs}} = {R_1} + {R_2} + ... + {R_n}$where${R_{eqs}}$ is the equivalent resistance of resistors in series and ${R_1}....{R_n}$ are the individual resistances.
Complete step by step answer
![seo images](https://www.vedantu.com/question-sets/cd8dcd7c-f161-49fd-880d-f5623b418e004351483997869682510.png)
The figure above shows the wire after it has been made into a square with the sixteen ohms resistor connected across the two corners of the square. This configuration resembles a Wheatstone bridge as shown in the figure below in a more familiar setting
![seo images](https://www.vedantu.com/question-sets/cb308c5f-3517-47c8-bd72-a35c2d23ecd76084552253838788124.png)
To calculate the equivalent resistance, we assume a voltage is applied at any of the opposite corners of the square. This is allowed because all resistances are equal.
Let’s say we placed the voltage at the opposite corners to where the 16 Ohms resistor is connected. Since, it is a balanced Wheatstone bridge, the voltage across the 16 Ohms is zero. Hence, we can ignore the 16 Ohms resistance. The two resistance at the top are in series, likewise the two at the bottom. Hence,
For top resistance
$\Rightarrow {R_{eq1}} = {R_1} + {R_2} = 4 + 4 = 8\Omega $
For bottom resistance, similarly,
$\Rightarrow {R_{eq2}} = 4 + 4 = 8\Omega $,
This two resistance are in parallel, and hence calculated as
$\Rightarrow \dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_{eq1}}}} + \dfrac{1}{{{R_{eq2}}}} = \dfrac{1}{8} + \dfrac{1}{8}$
Computing we have that
$\Rightarrow \dfrac{1}{{{R_{eq}}}} = \dfrac{1}{4}$
$\Rightarrow {R_{eq}} = 4\Omega $
Hence, the correct option is D.
Note
To avoid confusions, we are allowed to assume a voltage across the opposite corners because from the definition of equivalent resistance of a circuit, it is the one resistance to the current flow in a circuit which can replace all the resistances in the circuit. Since the voltage across 16 Ohms is zero, no current flows through the resistor, and thus does not count to the equivalent resistance.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)