Figure, shows a network of eight resistors numbered 1 To 8 ,...

Figure, shows a network of eight resistors numbered 1 To 8 , each equal to $2 \Omega$, connected to a $3 \mathrm{~V}$ battery of negligible internal resistance The current $\mathrm{I}$ in the circuit is .... (A) $0.25 \mathrm{~A}$ (B) $0.5 \mathrm{~A}$ (C) $0.75 \mathrm{~A}$ (D) $1.0 \mathrm{~A}$

Figure, shows a network of eight resistors numbered 1 To 8 , each equal to $2 \Omega$, connected to a $3 \mathrm{~V}$ battery of negligible internal resistance The current $\mathrm{I}$ in the circuit is ....
(A) $0.25 \mathrm{~A}$
(B) $0.5 \mathrm{~A}$
(C) $0.75 \mathrm{~A}$
(D) $1.0 \mathrm{~A}$

Key Concepts

Equivalent Resistance Calculation

Equivalent resistance calculation involves combining series and parallel resistor configurations to simplify complex circuits into a single resistor. This method is essential for analyzing circuits, as it enables the application of Ohm's Law and other circuit principles to determine overall circuit behavior, such as the total current supplied by a power source.

Ohm's Law

Ohm's Law is fundamental in circuit analysis and states that the voltage across a resistor is equal to the product of the current flowing through it and its resistance (V = IR). This relationship is essential for determining unknown quantities in a circuit, such as the current or voltage, once the other values are known.

Series Resistors

Series resistors are connected one after the other such that the same current flows through each resistor. The total or equivalent resistance of resistors in series is obtained by summing their individual resistances. This concept simplifies circuit analysis by allowing multiple resistors to be replaced with a single equivalent resistor.

Parallel Resistors

When resistors are connected in parallel, they share the same voltage across them and the total current is distributed among the parallel branches. The equivalent resistance decreases as more resistors are added and is determined by the reciprocal sum of the reciprocals of the individual resistances. This is crucial for analyzing circuits where resistors split the current.

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