Buggé: DC Circuits 4
Equivalent Resistance
Did you know?
Series resistance: When resistors are connected in series, the current through each resistor is the same
and the potential difference across the resistors is the sum of the potential differences across each
resistor:
I1 = I2 = I3 = Itotal
ΔV1 + ΔV2 + ΔV3 = ΔVtotal
The total equivalent resistance of electric resistors in series is just the sum of the resistances of the
different resistors:
Requivalent = R1 + R2 + R3 + …
where R1, R2, R3, … are the resistances of the resistors that are connected in series.
Parallel resistance: When resistors are connected in parallel, the potential difference is the same across
each resistor and the total electric current is the sum of the currents through each resistor:
ΔV1 = ΔV2 = ΔV3 and I = I1 + I2 + I3
The total equivalent resistance of electric resistors in parallel is determined using the equation:
1/Requivalent = 1/R1 + 1/R2 + 1/R3
4.1 Draw a circuit in which there are three resistors of R1 and the total resistance of the circuit is 3R1.
4.2 Draw a circuit in which there are two resistors of R1 and the total resistance of the circuit is ½ R1.
4.3 Matt says that the total resistance of any number of resistors in series is always bigger than the
resistance of each resistor, and the total resistance of any number of resistors in parallel is always
smaller than the resistance of the smallest resistor. Does his claim make any sense to you? If not, come
up with the ways to rule it out.
Buggé: DC Circuits 4
4.4 Four circuits are shown below. Draw an equivalent simplified circuit for each and find the total
resistance. Each resistor has a resistance R.
Circuit
Equivalent Circuit
Total Resistance
a)
b)
c)
d)
4.5 What is the total resistance of
the circuit to the right? What is the
total current?
4.6 You have a box full of 50-Ω and 100-Ω resistors. For a circuit board that you are building, you need
three 25-Ω resistors and two-125 Ω resistors. Decide what you need to do to make the resistors for this
circuit board.