Question

The current in the coil of resistance 90 ohms is to be reduced by $90$ percent.What value of resistance should be connected in parallel with it ?

Answer 1

When resistors are connected in series then equivalent resistance is equal to: ${{R}_{eq}}={{R}_{1}}+{{R}_{2}}+{{R}_{3}}+{{R}_{4}}+.....$ and when resistors are connected in parallel the equivalent resistance is equal $\dfrac{1}{{{R}_{eq}}}=\dfrac{1}{{{R}_{1}}}+\dfrac{1}{{{R}_{2}}}+\dfrac{1}{{{R}_{3}}}+\dfrac{1}{{{R}_{4}}}+...$

Complete step by step answer:
First, we understand about the resistance and its type:
Resistance: It tells us about the amount of current flow through the given interval of time. Its S.I unit is ohm. It is of two types: series and parallel resistance.
Series resistance: In a series circuit, the output current of the first resistor flows into the second resistor, therefore the current is same in each resistor and voltage across each resistor is different.
${{R}_{eq}}={{R}_{1}}+{{R}_{2}}+{{R}_{3}}+{{R}_{4}}+.....$

Parallel resistor: In parallel circuit the voltage across each resistor is the same, but current is different along each resistor.
$\dfrac{1}{{{R}_{eq}}}=\dfrac{1}{{{R}_{1}}}+\dfrac{1}{{{R}_{2}}}+\dfrac{1}{{{R}_{3}}}+\dfrac{1}{{{R}_{4}}}+...$
Shunt: it is a device which allows electric current to pass around another point in the circuit by creating a low resistance path. It can be calculated by: s = $\dfrac{G}{(n-1)}$.

Now according to the question: We know that the reduced current should pass through shunt (a type of resistance) or the resistance that is connected in parallel. As resistance connected in parallel. hence, voltage across the required resistance S and $90ohm$ resistance is same, i.e.,
${{i}_{g}}=\dfrac{i}{10}$
Required shunt (s) = $\dfrac{G}{(n-1)}=\dfrac{90}{(10-1)}=10\,ohm$.

Hence, $10\,ohm$ resistance is required to be connected in parallel.

Note: In such type of question, you have to apply the concepts of shunt and the formula related to it i.e., s = $\dfrac{G}{(n-1)}$and also you have to keep the concepts related to resistance and their types (like series resistance and parallel resistance).