Question

Which of the following circuits has the smallest equivalent resistance?The value of the last resistance in the fourth circuit is 2 ohm.

Answer 1

Given:

Four circuit diagrams of the resistance are shown in the question.

To find:

The circuit with the smallest equivalent resistance

Step-by-step explanation:

The equivalent resistance in the first circuit is,

`\begin{gathered} 2+2\text{ \lparen series combination\rparen} \\ =4\text{ ohm } \end{gathered}`

The equivalent resistance of the second circuit is,

`\begin{gathered} (1)/(R)=(1)/(2)+(1)/(2)\text{ \lparen parallel combination\rparen} \\ (1)/(R)=(2)/(2) \\ R=1\text{ ohm} \end{gathered}`

The equivalent resistance of the third circuit is,

`\begin{gathered} 2+2+2+2\text{ \lparen series\rparen} \\ =8\text{ ohm} \end{gathered}`

The equivalent resistance of the third circuit is,

`\begin{gathered} (1)/(R^(\prime))=(1)/(2)+(1)/(2)+(1)/(2)+(1)/(2) \\ (1)/(R^(\prime))=(4)/(2) \\ R^(\prime)=(2)/(4) \\ R^(\prime)=(1)/(2)\text{ ohm} \end{gathered}`

Hence, the circuit with the smallest resistance is the fourth circuit where four resistances are in parallel combination.