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Circuits
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Series Circuit

A circuit with only one path for the
electrons to flow.
Parallel Circuit

A circuit with multiple paths for the
electrons to flow.
Kirchoff’s Laws of Circuits
Kirchoff’s Voltage Law
 Based on Law of Conservation of
Energy
 V=W/q
 Potential difference is related to
energy and work.
 The total voltage drops (energy used)
must be equal to the total energy
supplied in the circuit
Kirchoff’s Current Law
 Based on conservation of charge.
 The total current going into a junction
must be equal to the current going out
of the junction.
2A
3A
1A
Mountain River Analogy

Circuits are like mountain rivers. No matter
what path they take the distance from the
top of the mountain to the plain is the same
and the amount of water flowing down the
mountain is the same.
 When a river splits into two paths that is like
a parallel circuit. The total amount of water
is equal to the sum of the water flowing in
each path.
 A resistor would be like a narrow section of
the river that causes rapids.
 A battery is the potential energy based on
the height on the mountain that the river
starts.
Series Circuit

Since there is only one path for the current
with no junctions,we can say the current (I)
remains constant throughout.
IT = I1 = I2 ……..
 The equivalent resistance is the sum of all
the resistances.
Req = R1 + R2………
 Since voltage drops occur across
resistances, the sum of the drops equals the
total voltage supplied
VT = V1 + V2 ……..
Parallel Circuit
The potential difference (V) will remain
the same across all paths.
VT = V1 = V2 = V3 ……
 Based on Kirchoff’s Law, because
there are many junctions, the current
into the junctions equal to the current
coming out of the junctions.
IT = I1 + I2 + I3 …..

Resistance in a Parallel Circuit
Combining parallel circuit laws with Ohm’s
Law, we can formulate an equation for the
equivalent resistance of a parallel circuit.
1/Req = 1/R1 + 1/R2 + 1/R3 …..
Based on Ohm’s Law
 I1 = V1/R1
I2 = V2/R2 I3 = V3/R3
Applying Kirchoff’s Law
 VT/Req = V1/R1 + V2/R2 + V3/R3
Since voltage is constant at any point in a parallel
circuit.
 1/Req = 1/R1 + 1/R2 + 1/R3

Measurements in Circuits
Voltmeter - must be wired in parallel.
Measures the drop in potential
difference across the two leads
 Ammeter - must be wired in series with
the circuit. Will measure the current in
that leg of the junction.
 Resistance - must be calculated based
on voltage and current readings.

Series Practice

a.
b.
Two resistors, 47.0 ohms and 82.0
ohms, are connected in series across
a 45.0V battery.
What is the current in the circuit?
What is the voltage drop across each
resistor?
Parallel Practice

a.
b.
c.
Three resistors 60.0 ohms, 30.0
ohms, and 20.0 ohms are connected
in parallel across a 90.0V battery.
Find the current through each branch
of the circuit.
Find the equivalent resistance of the
circuit.
What is the current from the battery?