Resistance in Series
Suppose a circuit is connected in series as shown in the figure above, with resistances at different sections: R1, R2, and R3.
Let current I flow through the network, and voltage across R1, R2, and R3 be V1, V2, and V3 respectively.
According to Ohm’s Law:
V = I × R ..........(i)
From the circuit:
V = V1 + V2 + V3 ..........(ii)
V = IR1 + IR2 + IR3 ..........(iii)
V = I(R1 + R2 + R3) ..........(iv)
From equation (i) and (iv):
IR = I(R1 + R2 + R3) ..........(v)
R = R1 + R2 + R3
Hence, the equivalent resistance in a series circuit is the **sum of all individual resistances** connected in series.
Characteristics of Resistance in Series:
- The same current flows through each resistor.
- Voltage drop across each resistor is different.
- Power is additive.
Resistance in Parallel
Suppose a circuit is connected in parallel as shown above, with resistances R1, R2, and R3 in each branch.
Let voltage V be applied across the network and the currents through R1, R2, and R3 be I1, I2, and I3 respectively.
According to Ohm’s Law:
V = I × R ..........(i)
From the circuit:
I = I1 + I2 + I3 ..........(ii)
I = V/R1 + V/R2 + V/R3 ..........(iii)
I = V(1/R1 + 1/R2 + 1/R3) ..........(iv)
From equation (i) and (iv):
V/R = V(1/R1 + 1/R2 + 1/R3) ..........(v)
1/R = 1/R1 + 1/R2 + 1/R3
For two parallel resistors:
R = (R1 × R2) / (R1 + R2)
Characteristics of Resistance in Parallel:
- The voltage remains the same across all resistors.
- Current through each resistor is different depending on resistance value.
- Power is additive.