Download Ohm`s law for series and parallel circuits

Kirchoff’s
Circuit Law
Part 1: Current
Kirchoff’s circuit law
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Garden Analogy: Imagine a garden
path. The paths are one-way.
People don’t stop and walk at the
same speed.
Imagine there are 2, 3, and 4 people
walking down the yellow path. They
meet at the blue path at the same
time.
How many people will walk down
the blue path?
9 people enter the path, 9 people will
walk through the path, 9 people will exit
3
4
2
Picture source: http://www.fnsg.org/conceptual-site-plan/
Kirchoff’s circuit law
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In 1845, Kirchoff realized that
electrons in a circuit are not
made or destroyed. They are
conserved.
At any point, the number of
electrons entering = the number
of electrons leaving.
Sum of current entering = sum of
current leaving
I1 + I2 + I3 = I4
I3
I2
I1
I4
Picture source: http://www.fnsg.org/conceptual-site-plan/
Kirchoff’s circuit law
Kirchoff’s circuit law:
Sum of current entering = Sum of
current leaving
What equation can you make will
this parallel circuit?
I1 = I2 + I3
I1
I2
I3
Ohm’s law for parallel circuits
Is I4 and I5 the same?
Yes!
I5
I1
I3
I2
I4
Current in Series Circuit
Think about it: For a circuit in series, is
current equal at all points? Or are the
values of I1, I2, and I3 different?
I3
I2
The current is at the same at all point!
I1 = I2= I3
Explanation: There is only one path, so
all the electrons have to move at the
same speed.
Kirchoff’s circuit law also proves it!
I1
Ohm’s Law
Part 2: Voltage
Ohm’s Law
Who can remember Ohm’s Law?
V=IxR
What is the current in this circuit?
Ohm’s law is different for circuits in series or parallel.
Voltage in Series Circuit
When there are multiple batteries in series, the total voltage is the sum of all the
voltages.
V_total = V1 + V2 + V3
What is the total voltage in this circuit?
V_total = 6V + 3V + 4V = 13 Volts
Voltage in parallel circuits
Voltage is the same in parallel
circuits.
V_total = V1 = V2 = V3
Recap for voltage
Series: The total voltage is the sum of all
voltages.
Parallel: Voltage is the same everywhere!
Adding a battery in parallel does not
change the voltage.
Picture source:http://www.dynamicscience.com.au/tester/solutions1/electric/batteriesincircuits1.htm
Ohm’s Law
Part 3: Resistance
Resistance in Series Circuit
When there are multiple resistors in a row, the total resistance is the sum of all the
resistors in a row.
R_total = R1 + R2 + R3 + ….
For the below circuit, there are 3 resistors in a row. So you add all 3 of them together!
Resistance in Series Circuit
Takmela measured the voltage to be 12 V.
What is the current in this circuit?
Step 1: Make it one resistor instead of two!
4 Ω + 2 Ω = 6 Ω = Total resistance
Step 2: Use Ohm’s Law
V=IxR
12 V = I x 6 Ω
I = 2 Amps
Resistance in Parallel Circuits
For each resistor, an additional term is
added to the right side of the equation.
Resistance in Parallel Circuits
What is the total resistance in this circuit?
1) How many resistors are in parallel?
Since there are only 2 resistors, the equation becomes:
Resistors in Parallel
2) Now fill in the values for the two resistors
3) Add the two fractions together
Resistors in Parallel
So now we have:
Since there is only 1 fraction on each side of the
equation, we can flip it!
Recap
Part 4
Recap:
Remember: This is just for components that are in series!
SERIES
Total?
Equation
form!
Voltage
Add
V1 + V2 +...
Current
Equals
I1 = I2 =...
Resistance
Add
R1 + R2 +...
Recap for Parallel Circuits
Remember: This is just for components that are in parallel!
Parallel
Total?
Equation form!
Voltage
Equals
V1 = V2 =...
Current
Adds
Kirchoff’s law
For resistance: