simply the product of the current and the resistance. The voltage drop across the two
resistors is:
Note that the voltage drop across the two resistors is 10 V + 20 V = 30 V, which is the
total voltage drop across the circuit.
Resistors in Parallel
Two resistors are in parallel when the circuit splits in two and one resistor is placed on
each of the two branches.
In this circumstance, it is often useful to calculate the equivalent resistance as if there
were only one resistor, rather than deal with each resistor individually. Calculating the
equivalent resistance of two or more resistors in parallel is a little more complicated than
calculating the total resistance of two or more resistors in series. Given two resistors,
and , in parallel, the equivalent resistance, , is:
When a circuit splits in two, the current is divided between the two branches, though the
current through each resistor will not necessarily be the same. The voltage drop must be
the same across both resistors, so the current will be stronger for a weaker resistor, and
vice versa.
EXAMPLE
Two resistors, = 5 and = 20 , are set up in parallel, as in the diagram above. The
battery produces a potential difference of = 12 V. What is the total resistance in the
circuit? What is the current running through and? What is the power dissipated in the
resistors?WHAT IS THE TOTAL RESISTANCE IN THE CIRCUIT?
Answering this question is just a matter of plugging numbers into the formula for
resistors in parallel.