Question

Calculate equivalent resistance when three resistances of 2 ohms, 3 ohms and 6 ohms are connected in parallel combination.

Answer 1

Hint: Two types of circuits are known-one is series circuit and other one is parallel circuit. In a parallel circuit combination of resistors, the ends of each of the resistances are connected to the same common point. . It is to be noted that if more resistances are connected in parallel, the effective resistance of the circuit will decrease and current will increase. But in series circuits if more resistances are connected then effective resistance will increase and current will decrease.

Complete step by step solution:
The first thing to understand about parallel combination of circuits is that the voltage is equal across all three resistances in the circuit. This is because voltage measured between common points must always be the same at any given time. The reason is that the value of resistance in parallel combination is negligible or is less than the individual resistance. But the value of current is different for all the resistances. The total current is equal to the sum of current through each individual resistance.
Given three resistances are
\[{R_1} = 2\Omega \]
\[{R_2} = 3\Omega \]
\[{R_3} = 6\Omega \]

Formula used to calculate equivalent resistance for the parallel combination of resistances is:
\[\Rightarrow \dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}\]
Substituting given values and solving, above equation
\[\Rightarrow \dfrac{1}{R} = \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{6}\]
\[\Rightarrow \dfrac{1}{R} = \dfrac{{3 + 2 + 1}}{6}\]
\[\Rightarrow \dfrac{1}{R} = \dfrac{6}{6}\]
\[\Rightarrow \dfrac{1}{R} = 1\Omega \]
\[\Rightarrow R = 1\Omega \]
It is mandatory to inverse the value of ‘R’ in the denominator while finding the equivalent resistance in parallel combination. The value of equivalent resistance of three resistances connected in parallel is \[ 1\Omega \]. In case if a circuit is connected in parallel the appliances work efficiently. But if one of the appliances in this circuit is fused, the current continues to flow from the other.

Note: The parallel combination works in accordance with Ohm’s Law \[(V = IR)\]. But since current varies, Ohm’s law is applied to find the value of current I for all the resistances. Because resistance and voltage will already be given. The value of individual current can be known by using formula \[I = \dfrac{V}{R}\].