However, each resistor causes a voltage drop, and if there is more than one resistor in the
circuit, the sum of the voltage drops across each resistor in the circuit is equal to the total
voltage drop in the circuit. The total resistance in a circuit with two or more resistors in
series is equal to the sum of the resistance of all the resistors: a circuit would have the
same resistance if it had three resistors in series, or just one big resistor with the
resistance of the original three resistors put together. In equation form, this principle is
quite simple. In a circuit with two resistors, and , in series, the total resistance,
is:
EXAMPLE
In the figure above, a battery supplies 30 V to a circuit with a 10 resistor and a 20
resistor. What is the current in the circuit, and what is the voltage drop across each resistor?WHAT IS THE CURRENT IN THE CIRCUIT?
We can determine the current in the circuit by applying Ohm’s Law: I = V/R. We know
what V is, but we need to calculate the total resistance in the circuit by adding together
the individual resistances of the two resistors in series:
When we know the total resistance in the circuit, we can determine the current through
the circuit with a simple application of Ohm’s Law:
WHAT IS THE VOLTAGE DROP ACROSS EACH RESISTOR?
Determining the voltage drop across an individual resistor in a series of resistors simply
requires a reapplication of Ohm’s Law. We know the current through the circuit, and we
know the resistance of that individual resistor, so the voltage drop across that resistor is