Department of Engineering Science and Physics
ENS 136
Assignment 2: Analysis of series and parallel combinations of
resistive circuits.
Resistances in series: A set of resistors will be connected is series if the same
current passes through all the resistors. The total resistance of the series
combination of resistors is the sum of individual resistors.
Compute the equivalent (total) resistance of the circuit shown in Fig. 1.
Figure 1.
Equivalent resistance RE = R1 + R2 = ______________
Current provided by the voltage source IS = VS/RE = ______________
V1 = I1 x R1 = _______________
V2 = I1 x R2 = _______________
V1 + V2 = ________________
Do you see any relationship between VS and V1 and V2? Please explain.
Fall 2010
Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Compute power dissipated by R1
P1 = V1 x I1 = ________________
Power can also be computed as:
P1 = I12 x R1 = ________________
and
P1 = V12/R1 = _________________
Compute power dissipated by R2
P2 = V2 x I1 = ________________
also
P2 = I12 x R2 = ________________
and
P2 = V22/R2 = _________________
Compute power delivered by the voltage source:
PS = VS x IS = __________________
Do you see any relationship between power delivered by the voltage source and
the power dissipated by the resistors R1 and R2? Please explain.
Now measure the equivalent resistance of the circuit in Fig. 1. Note that you’ll
measure the equivalent resistance with respect to the source terminals.
Disconnect the voltage source and connect the Ohmmeter at those terminals.
Record your measurement below.
RE = ____________
Fall 2010
Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Is the measure RE is the same as the computed RE?
Now measure the current IS and voltage V1 and V2 (see the circuit diagram in
Figure 2).
Figure 2.
IS = ___________
V1 = ______________
V2 = _______________
Are the measured values of the current IS and voltage V1 and V2 the same as
their computed values?
Now measure the power delivered by the source PS, power dissipated by the
resistor R1 (P1) and the power dissipated by the resistor R2 (P2) (see the circuit
diagram in Figure 3).
PS = ___________
P1 = ______________
P2 = _______________
Are the measured values of PS, P1 and P2 the same as their computed values?
Fall 2010
Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Figure 3.
Resistances in parallel: A set of resistors are connected is parallel if the same
voltage appears across all the resistors. The reciprocal of equivalent (total)
resistance of the parallel combination of resistors is the sum of reciprocals of the
individual resistors.
Compute the equivalent (total) resistance of the circuit shown in Fig. 4.
Fall 2010
Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Figure 4.
Note that R2 and R3 are in parallel and the parallel combination of R2 and R3 is in
series with R1.
First find the equivalent resistance of the parallel combination of R2 and R3
1/RE23 = 1/R2 + 1/R3
RE23 = ______________
Equivalent resistance RE = R1 + RE23 = ______________
V1 = IS x R1 = _______________
V2 = IS x RE23 = _______________
V1 + V2 = ________________ = VS
Current provided by the voltage source IS = VS/RE = ______________
Current through R2 = I2 = V2/R2 = ______________
Current through R3 = I3 = V2/R3 = ______________
What is the current through R1? I1 = _______________
Compute power dissipated by R1
P1 = V1 x I1 = ________________
Power can also be computed as:
P1 = I12 x R1 = ________________
and
P1 = V12/R1 = _________________
Compute power dissipated by R2
P2 = V2 x I2 = ________________
also
P2 = I22 x R2 = ________________
Fall 2010
Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
and
P2 = V22/R2 = _________________
Compute power dissipated by R3
P3 = V2 x I3 = ________________
also
P3 = I32 x R3 = ________________
and
P3 = V22/R3 = _________________
Compute power delivered by the voltage source:
PS = VS x IS = __________________
Do you see any relationship between power delivered by the voltage source and
the power dissipated by the resistors R1, R2, and R3? Please explain.
Now measure the equivalent resistance of the circuit in Fig. 4. Record your
measurement below.
RE = ____________
Is the measure RE is the same as the computed RE?
Now measure the current IS , I2, I3, and voltage V1 and V2 (see the circuit diagram
in Figure 5).
Fall 2010
Syed A. Rizvi
Department of Engineering Science and Physics
ENS 136
Figure 5.
IS = ___________, I2 = ______________, I3 = ______________
V1 = ______________
V2 = _______________
Are the measured values of the current IS,I2, I3, and voltages V1 and V2 the same
as their computed values?
Now measure the power delivered by the source PS, power dissipated by the
resistor R1 (P1), the power dissipated by the resistor R2 (P2), and the power
dissipated by the resistor R3 (P3).
PS = ___________ P1 = ______________
P3 = _______________
P2 = _______________
Are the measured values of the PS, P1, P2 and P3 the same as their computed
values?
Fall 2010
Syed A. Rizvi