# Four resistances R1 = 1 Om R2 = 2 Om R3 = 3 Om R4 = 4 Om are connected according

Four resistances R1 = 1 Om R2 = 2 Om R3 = 3 Om R4 = 4 Om are connected according to the diagram. Find the total resistance of the circuit.

Given:

R1 = 1 Ohm – the value of the first resistance;

R2 = 2 Ohm – the value of the second resistance;

R3 = 3 Ohm – the value of the third resistance;

R4 = 4 Ohm – the value of the fourth resistance.

It is required to determine R (Ohm) – the total resistance of the circuit.

Since the type of connection is not indicated in the condition of the problem, we will find the total resistance of the circuit for two cases:

a) With a series connection of all resistances:

R = R1 + R2 + R3 + R4 = 1 + 2 + 3 + 4 = 3 + 3 + 4 = 6 + 4 = 10 ohms.

b) With parallel connection of all resistances:

1 / R = 1 / R1 + 1 / R2 + 1 / R3 + 1 / R4;

1 / R = 1/1 + 1/2 + 1/3 + 1/4;

1 / R = 1 + 6/12 + 4/12 + 3/12;

1 / R = 1 + 13/12 = 25/12;

R = 12/25 = 48/100 = 0.48 Ohm.

Answer: with a series connection, the total resistance of the circuit will be 10 ohms, with a parallel connection – 0.48 ohms.

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