Answer

Verified

419.1k+ 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.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What organs are located on the left side of your body class 11 biology CBSE