Very Short Question and Answers - Resistance of a System of Resistors

We combine resistors to obtain a required total or 'effective' resistance that may not be available as a single resistor and to control the current and voltage in different parts of the circuit.

A series combination is when resistors are connected end-to-end so that the same current flows through each resistor.

The total resistance R = R1 + R2 + R3.

The total resistance increases; it is the sum of the individual resistances.

Total resistance = 2 Ω + 3 Ω + 5 Ω = 10 Ω.

The same current flows through all resistors in a series circuit.

If one resistor fails (breaks) in series, the circuit is broken and the current stops; all devices connected in series go off.

Resistors are in parallel if they are connected such that both ends are joined at the same two points, making the voltage across each resistor the same.

1/R = 1/R1 + 1/R2 + 1/R3.

The total resistance in parallel is always less than the smallest resistance of the resistors used.

1/R = 1/4 + 1/4 = 2/4 = 1/2, so R = 2 Ω.

The total current divides among the parallel branches according to the resistance of each branch.

1/R = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1, so total resistance R = 1 Ω.

The voltage across each resistor is 6V; all resistors in parallel have the same voltage across them.

Festoon lights or serial decorative bulbs are examples; if one bulb fails, the whole string turns off.

Electrical sockets and home appliances are connected in parallel so that each receives the same voltage and can function independently.

Use series combination to increase total resistance or to decrease current in a circuit.

Use parallel combination to decrease resistance, obtain a higher current, or to provide the same voltage to each device.

Only that branch stops working; current continues in the other branches, so the rest of the circuit keeps operating.

In series: current is same through all resistors, voltage divides. In parallel: voltage is same across all resistors, current divides.