Resistor calculations | series and parallel circuits

According to Ohms law, the voltage drop across a resistance is directly proportional to the current flowing through it, V ∝ I.

I  – The amount of current through the resistor in the unit of amperes.

V – Voltage drop across the resistor.

R – Resistance.

Mathematically it can be written as V = I * R.

Current vs Voltage graph

The V-I characteristic curve of a resistor has a linear relationship between voltage and current.

It has a constant slope, m = V/I = R = tan(θ) .

Current, Power, Energy calculations.

Power is the work done per unit time, P = V I = I2 R = V2/R, unit of power is watts or joule per second (J/s).

The energy dissipation as heat, H = work = power x time =  V I t = I2 R t= V2/R t, unit  is Joule.

Resistors in series and parallel circuits

Voltage division of resistors in a series circuit

In a series resistor network, the total input voltage will be divided across each resistor in proportional to their value of resistance. In a series connection, the current through all the resistors is the same. So for an N number of resistors R1, R2, R3,…RN, the corresponding voltage drop is equal to V1, V2, V3…VN. As the current ‘ I ‘  is the same for all resistors, the value of V1 = I x R1, V2= I x R2, V3= I x R3, … VN = I x RN.

The current I = V / R1 + R2 + R3 + … + RN.

For example, V1 = I x R1 = V x R1 / R1 + R2 + R3 + … + RN

Hence the equation becomes, the voltage across an individual resistor is the product of total voltage and the ratio of that resistance to the total resistance of the series network.

Current division in a parallel resistor circuit

In a parallel circuit, the voltage across the resistors is the same. But the current through each resistor varies with its resistance.

The current through parallely connected resistors R1, R2, R3… RN is equal to  I1 = V/ R1, I2 = V/ R2, I3 = V/ R3,…., IN = V/ RN