Question

Calculate the equivalent resistance between the points A and B as per the figure $\left( \text{in }\Omega \right)$

$\begin{aligned} & A.\dfrac{1}{5} \\\ & B.1\dfrac{1}{4} \\\ & C.2\dfrac{1}{3} \\\ & D.3\dfrac{1}{2} \\\ \end{aligned}$

Answer 1

The equivalent resistance of a series circuit can be found by taking the sum of each value of the resistance included in the circuit. The equivalent resistance of a parallel circuit can be found by taking the sum of the reciprocal of the values of each resistances. This all will help you in solving this question.

Complete step by step answer:
Here the resistance of wire CE & DF is zero. Point C & E and point D & Fare brought close to each other because of identical potential at C & E also D & F. That is the figure can be represented as,

Here we can see that resistance between the points EF, ED and CD are in parallel.
$r=1\parallel 1\parallel 1$
Therefore the equivalent resistance among this points can be written as,
$r=\dfrac{1}{1}+\dfrac{1}{1}+\dfrac{1}{1}=\dfrac{1}{3}\Omega$
Now we can redraw the diagram as,

Here the equivalent resistance can be found easily. The three resistance are now found to be in series. Therefore we can write that,
The resistance across AB can be written as,
${{R}_{AB}}=1+1+\dfrac{1}{3}=2+\dfrac{1}{3}=2\dfrac{1}{3}\Omega$

Therefore the resistance has been obtained. It has been mentioned as option C.

Note:
The load connected in a circuit which is also referred to as a resistor is used to convert the electrical energy into some other form of energy. It can be a light source or an electric motor or anything else. When there is no load connected in the circuit, then the circuit will be short circuited. In series circuit electrons can travel in unidirectional only. Here the current will be the equivalent in all the resistors connected. And also the voltage across the resistor will be different. In parallel connection the voltage across the resistors will be the same but the current differs.