Combined Series and Parallel Circuits
Objectives:
1. Calculate the equivalent resistance, current, and voltage of series and parallel circuits.
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2. Calculate the equivalent resistance of circuits combining series and parallel connections.
3. To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit problem.
4. Solve circuit problems.
Resistance and Current
Resistance and Current
Series Circuit
•Equivalent resistance is equal to the sum of all the resistance in the circuit.
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•Circuit current is equal to the voltage source divided by the equivalent resistance.
the equivalent resistance.
Req = R1 + R2 + R3 + Rn...
I = Vsource / Req
Resistance and Current – Series Circuit
Resistance and Current Series Circuit
V = 12 volts
R1 = 10 Ω
R2 = 25 Ω
Find the equivalent resistance
Find the current through the circuit
Find the voltage through each resistor
Resistance and Current Parallel Circuit
Resistance and Current Parallel Circuit
Parallel Circuit
Parallel
Circuit
•The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.
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•The total current is the sum of all the currents.
•The potential difference across each resistor is the same
1/ Req = 1/ R1 + 1/ R2 + 1/ Rn...
I = I1 + I 2 + I n.....
I1 = Vsource / R1
Resistance and Current – Parallel Circuits
V = 12 volts
V
= 12 volts
R1 = 10 Ω
R2 = 25 Ω
What is the voltage through each resistor?
Find the equivalent resistance
Find the current through R1 and R2
Household circuits
Household circuits
Why do the lights dim when the hair dryer goes on?
Small resistance from wiring
This is called a combination series and parallel circuit
Series and Parallel Circuits
Series and Parallel Circuits
1. Draw a diagram of the circuit
2. Find any resistors in parallel. They must have the same potential difference across them. Calculate the single equivalent resistance of a resistor that can replace them.
3. Are any resistors (including the parallel equivalent resistor) in series? Resistors in series have one and only one current path through them. Calculate the new single equivalent resistance that can replace them. Draw a new schematic diagram using that resistor.
4. Repeat steps 2 and 3 until you can reduce the current to a p
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single resistor. Find the total circuit current. Then go backwards to find the currents through and the voltages across individual resistors.
Kirchhoff’ss Rules
Kirchhoff
Rules
•
Kirchhoff's first law when officially stated sounds more complicated than it actually is Generally speaking, it says, the total current entering a actually is.
Generally speaking it says the total current entering a
junction must equal the total current leaving the junction. After all, no charges can simply disappear or get created, so current can't disappear or be created either. A junction is any place in a circuit where more than two paths come together
two paths come together. •
Kirchhoff s second law when officially stated sounds more complicated Kirchhoff's
second law when officially stated sounds more complicated
than it actually is. Generally speaking, it says, around any loop in a circuit, the voltage rises must equal the voltage drops. Another way of thinking about this is to consider that whatever energy a charge starts with in a circuit loop, it must end up losing all that energy by the time it gets to the
circuit loop, it must end up losing all that energy by the time it gets to the end. Or we could say that by the time a charge makes it to the end of a circuit, it must have given all its energy to do work.
Kirchhoff’ss Rules
Kirchhoff
Rules
Gustav Kirchhoff ‐ 1845
1. The sum of the currents entering any junction must equal the sum of the currents
junction must equal the sum of the currents leaving that junction. (junction rule)
In this example you will notice that 8
Amps of current enter the junction and
3 and 5 Amps leave the junction. This
makes a total of 8 Amps entering and 8
Amps leaving.
In this example you will notice 8 Amps
and 1 Amp entering the junction and 9
Amps leaving. This makes a total of 9
Amps entering and 9 Amps leaving.
In this example you will notice 8 Amps
and 1 Amp entering the junction while 7
Amps and 2 Amps leave. This makes a
total of 9 Amps entering and 9 Amps
leaving.
Kirchhoff’ss Rules
Kirchhoff
Rules
1 The
1.
The sum of the potential differences across sum of the potential differences across
all the elements around any closed circuit loop must equal zero (loop rule)
loop must equal zero. (loop rule)
This is a simple circuit showing the potential differences
across the source and the resistor. According to
Kirchhoff's 2nd law the sum of the potential differences
will be zero.
This diagram shows the potentials in the little circles
and then shows the potential differences off to the
side Notice that the potential difference is actually the
side.
difference between one potential and another. Moving
from a low potential to a high potential is considered a
potential rise or positive potential difference. Moving
from a high potential to a lower potential is considered a
potential drop or negative potential difference
difference.
This animation shows the same circuit as above but only
looks at the potential differences as you go around the
loop. Again, Kirchhoff's 2nd law says the sum of the
potential differences has to be zero
zero.