Question

A resistance of 0.01 ohms is connected in parallel with a resistance of one kilo ohms. Then the resistance of the combination will be?
A. 1000 ohms
B. 10 ohms
C. 1 ohm
D. 0.0099 ohm

Answer 1

Hint: We are given two resistance whose values are \[0.01\Omega \]and 1\[k\Omega \] that is 1000\[\Omega \]. Now, these two resistors are connected in parallel. We know broadly there are two methods of joining any component in an electric circuit that are series combination and parallel combination.

Complete step by step answer:
We know in parallel combination the voltage across the two resistors remains same and the equivalent resistance is given by the formula, \[R=\dfrac{{{R}_{1}}{{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}\]
The given values are \[{{R}_{1}}\]= \[0.01\Omega \] and \[{{R}_{2}}\]=1000\[\Omega \]
Substituting the values in the above mentioned equation we get,
$
R=\dfrac{0.01\times 1000}{0.01+1000} \\
\implies R=\dfrac{10}{1000.01} \\
\therefore R=0.0099\Omega \\
$
So, the value of the combination comes out to be 0.0099 ohms.

So, the correct answer is “Option D”.

Additional Information:
Resistors are said to be connected in parallel when both of their terminals are connected to each terminal of the other resistor. There is more than one path available to the current. They are also known as current dividers.

Note:
In this parallel combination the voltage across both of the resistors will always be the same but the current will get divided, also, one of the values was given in kilo ohms and so we have converted into ohms. Also, if one of the components in the parallel circuit gets fused, it does not affect the performance of other components in the circuit. This is one of the greatest advantages of parallel combination.