Download Kirchhoff`s laws and drift velocity File

Kirchhoff’s Laws
Objective: to recall Kirchhoff’s laws and use
them to solve problems.
Starter: what is the current and voltage in these
circuits? Mark the homework
Kirchhoff’s first law
The German physicist Gustav Kirchhoff established two laws which help us to understand
the function of electric circuits.
Kirchhoff’s first law states that:
The sum of the currents leaving any junction is always equal to the sum of the
currents that entered it.
This law is based upon the idea of the conservation of charge: no charge can be lost or
made in a circuit.
IIN
Thus the sum of the currents at a junction should be zero.
IIN = I1 + I2 … + In
ΣI = 0
I1
I3
I2
Using Kirchhoff’s first law
The energy in a circuit
What happens to the energy supplied to a circuit?
Batteries and power supplies supply electrical energy to a circuit. Devices within the
circuit transduce this energy: bulbs produce heat and light, resistors produce heat.
What is the conservation of energy?
Energy cannot be created or destroyed. All of the energy provided by a power supply
must be used by the circuit.
How does the voltage of a battery relate to the voltage measured across the devices in
a circuit?
Voltage is the energy transferred to the charge in a circuit. The battery’s voltage is shared
between the components, which transduce this energy into different forms.
Kirchhoff’s second law
Kirchhoff’s second law is based upon the law of the conservation of energy. It states that:
The total voltage across a circuit loop is equal to the sum of the voltage drops across
the devices in that loop.
Essentially, the energy you put into the circuit
equals the energy you get out of each circuit
loop.
VIN
I
An equation can be produced for each loop in
a circuit. For example:
VIN = V1 + V2
VIN = IR1 + IR2
V1
V2
R1
R2
Simple uses of Kirchhoff’s second law
Further uses for Kirchhoff’s law
Use Kirchhoff’s laws to find the values for each current.
E = 12 V
V1
10 Ω
V2
100 Ω
V3
40 Ω
As I =
V
R
I = 1.6 A
 There are 3 loops in the circuit. Each has a voltage
drop equal to the input voltage according to the 2nd
law.
I1
Therefore: E = V1 = V2 = V3
I
 The 1st law means that current entering each
junction equals the current leaving.
I2
I3
Therefore:
I=
12
10
12
+
100
I1 = 1.2 A
+
12
I = I1 + I2 + I3
I = 1.2 + 0.12 + 0.3
40
I2 = 0.1 A
I3 = 0.3 A
Current and drift velocity
Current is a flow of charge. Electrical devices
activate almost instantly once they are
supplied with power, however the electrons
actually move around a circuit quite slowly.
Their velocity is called drift velocity.
Current and drift velocity are linked by the following equation:
I = current (amps)
I = nAve
n = charged particles per unit volume
A = cross-sectional area (m2)
v = drift velocity (m/s)
e = charge on an electron (1.6 x 10-19 C)
Understanding I = nAve
Alternating current and direct current
RMS voltage
The voltage of AC can be viewed using an oscilloscope. There are three common voltage
measures, namely peak, peak-to-peak and RMS (root mean squared) voltage.
peak
voltage
RMS
voltage
peak-to-peak
voltage
zero
volts
RMS is a measure of the average magnitude of the
voltage.
VPEAK
VRMS
=
√2
RMS current and RMS power
To investigate voltage we use an oscilloscope connected across a resistor. As V  I, the
equation for calculating RMS current is similar to the equation for RMS voltage:
IRMS
=
IPEAK
√2
The equation for RMS power is a little different:
PPEAK = IPEAK × VPEAK
PRMS = IRMS × VRMS =
PPEAK
PRMS =
2
IPEAK
√2
VPEAK
×
√2
AC calculations
AC/DC summary