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Series and Parallel Circuits and the Three Cardinal Rules
for Solving Them
Series Circuits
Equivalent Resistance for a circuit is the defined as the single
resistance that could replace several resistors (components that
provide resistance). It can also be considered as the total
resistance of the circuit.
Kirchoff’s Voltage Law (Kirchoff’s Loop Rule) states that the
total voltage around a closed loop must be zero. In simpler
terms, it states that in a closed loop that the sum of the voltage
rises must be equal to the sum of the voltage drops.
Three Cardinal Rules for Circuits in a Series:
1. The total resistance in a series circuit (or equivalent
resistance) is equal to the sum of all the separate resistances.
OR
2. The current in all parts of a series circuit has the same
magnitude.
OR
3. Kirchoff’s Loop Rule (voltage law): the sum of all the separate
drops in potential around a series circuit (closed loop) is equal
to the potential rise of the battery (or power source).
OR
Example 1)
Series Resistance
A 6.00 Ω and a 4.00 Ω resistor are connected in series with a
12.0 V battery. We assume that the battery itself does not offer
any resistance to the circuit.
a. Draw a schematic diagram.
b. Find the equivalent (total) resistance for this circuit.
c. Find the current delivered to each resistor.
d. Find the power dissipated in each resistor.
e. Find the potential difference across each resistor.
Series and Parallel Circuits and the Three Cardinal Rules for Solving Them
Series Circuits
Equivalent Resistance for a circuit is the defined as the single resistance that could replace
several resistors (components that provide resistance). It can also be considered as the total
resistance of the circuit.
Kirchoff’s Voltage Law (Kirchoff’s Loop Rule) states that the total voltage around a closed
loop must be zero. In simpler terms, it states that in a closed loop that the sum of the voltage
rises must be equal to the sum of the voltage drops.
Three Cardinal Rules for Circuits in a Series:
1. The total resistance in a series circuit (or equivalent resistance) is equal to the sum of all the
separate resistances
.
OR
2. The current in all parts of a series circuit has the same magnitude.
OR
3. Kirchoff’s Loop Rule (voltage law): the sum of all the separate drops in potential around a
series circuit (closed loop) is equal to the potential rise of the battery (or power source).
OR
Example 1)
Series Resistance
A 6.00 Ω and a 4.00 Ω resistor are connected in series with a 12.0 V battery. We assume that
the battery itself does not offer any resistance to the circuit.
a. Draw a schematic diagram.
b. Find the equivalent (total) resistance for this circuit.
c. Find the current delivered to each resistor.
d. Find the power dissipated in each resistor.
e. Find the potential difference across each resistor.
Learning Activity 8.7
1. A 9-V battery is in a circuit with three resistors connected in series.
a. Draw a schematic diagram.
b. If the resistance of one of the resistors increases, how will the equivalent resistance
change?
c. What will happen to the current?
d. What will happen to the voltage of the resistor whose resistance was increased?
e. What will happen to the voltage of the battery?
2. A string of holiday lights has ten bulbs with equal resistance connected in series. When the string
of lights is connected to a 120-V outlet, the current through the bulbs is 0.06 A.
a. What is the equivalent resistance of the circuit?
b. What is the resistance of each bulb?
3. Two resistors are connect in series have a resistance of 47 and 82 ohms across a 45-V battery.
a. Draw a schematic diagram
b. What is the current in the circuit?
c. What is the voltage drop across each resistor?
d. If the 47 ohm resistor is replaced by a 39 ohm resistor, will the current increase, decrease,
or stay the same?
e. What is the new voltage drop across the 82 ohm resistor?
4. A series circuit is made up of a 12-V battery and three resistors. The voltage across one resistor
is 1.21 V, and the voltage across another resistor is 3.33 V.
a. What is the voltage of the third resistor?
b. If the first resistance of the first resistor is 3.2 Ohms, determine the resistance of the other
two resistors.
5. A 9-V battery and two resistors, 390 ohms and 479 ohms, are connected in series. What is the
voltage across the 470 ohm resistor? Draw a schematic diagram.
6. Three resistors of 3.3 kΩ, 4.7 kΩ, and 3.9 kΩ are connected in series across a 12-V battery.
a. What is the equivalent resistance?
b. What is the current through each resistor?
c. What is the voltage drop across each resistor?
d. What is the voltage rise?
e. What is the power of the circuit?
7. Draw a circuit diagram for three loads, connected in series to a battery, having resistances of 15
ohms, 24 ohms, and 36 ohms. If the current through the first load is 2.2 A, calculate:
a. The voltage drop across each of the loads
b. The voltage rise across the battery
c. The power for the circuit.
8. Two resistors are connected in series and have a resistance of 25 ohms and 35 ohms
respectively. The potential difference across the 25 ohm resistor is 65 V.
a. Calculate the potential difference across the 35 ohm resistor.
b. Calculate the potential rise of the battery.
c. Calculate the power for the 35 ohm resistor.
9. A string of 50 Christmas lights is connected in series to a 120 V line. Each light bulb has a
resistance of 1.6 ohms.
a. What is the total resistance of the lights?
b. What is the current flowing through the circuit?
c. What is the power of each light?
d. What would happen if the filament of one light burnt out?
Parallel Circuits
Kirchoff’s Junction Rule states that the sum of the currents coming in to a junction is equal to the
sum of the of the currents leaving the junction.
Example 2)
Parallel Resistance
A 6.00 Ω and a 4.00 Ω resistor are connected in parallel with a 12.0 V battery. We assume that
the battery itself des not offer any resistance to the circuit.
a. Draw the schematic diagram.
b. Find the equivalent (total) resistance for this circuit.
c. Find the potential difference across each resistor.
d. Find the current delivered to each resistor.
e. Find the power dissipated in each resistor.
f. Find the total power delivered to the resistors by the battery.