Page 765 - Mechatronics with Experiments

LABORATORY EXPERIMENTS 751
goes through the smaller resistor since there is smaller resistance to the flow of electrons.
For the voltage divider circuit

V (t) = V (t) + V (t) (11.6)
s
12
23
= R ⋅ i(t) + R ⋅ i(t) (11.7)
2
1
1
i(t) = V (t) (11.8)
s
R + R 2
1
R 1
V (t) = V (t) (11.9)
s
12
R + R 2
1
R 2
V (t) = V (t) (11.10)
s
23
R + R 2
1
The last two equations show how the voltage is divided between the series resistors.
For the current divider circuit,
V (t) = V (t) (11.11)
s
12
= R ⋅ i (t) (11.12)
1
1
= R ⋅ i (t) (11.13)
2 2
i(t) = i (t) + i (t) (11.14)
1 2
V (t) V (t)
s
s
= + (11.15)
R 1 R 2
( )
1 1
= + ⋅ V (t) (11.16)
s
R 1 R 2
R ⋅ R 2
1
V (t) = ⋅ i(t) (11.17)
s
R + R 2
1
= R ⋅ i (t) (11.18)
1
1
= R ⋅ i (t) (11.19)
2
2
R 2
i (t) = ⋅ i(t) (11.20)
1
R + R 2
1
R 1
i (t) = ⋅ i(t) (11.21)
2
R + R 2
1
Notice that the last two equations show how the current in the main line is divided over
the two parallel branches of resistors. Current measurement requires the measurement
instrument to be placed in series between the two points through which the current flow
is being measured. This requires disconnecting the circuit at a point, and inserting the
current measurement instrument (i.e., DMM in current measurement mode, ammeter) into
the circuit. Such circuit modifications are not always possible nor convenient. Another way
to measure current indirectly is to measure the voltage across a known resistor, then use
Ohm’s Law to calculate the current. If there is a resistor of known value at the circuit branch
that we want to measure current, then we can measure the voltage across it, and divide
the measured voltage by the resistor value to calculate the current that passes through that
resistor. This method is easier and accurate enough for us to use in the experiments.
Procedure
1. Using the digital multi-meter (DMM), measure the resistance and capacitance of a
few resistors and capacitors. Confirm your measurement with the specifications of
the component.