Note. Questa unità didattica è stata realizzata su lavagna LIM Hitachi per cui il formato originale era quello proprietario .yar.
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From Kirchhoff’s laws to equivalent resistor
Calculate the current I1 in the following circuit:
Using Ohm’s law we find:
And then for the first Kirchhoff’s law
It’s very easy.
Now, using the symbol notation find the potential difference between the two point A and B (VAB)
If we suppose to have a resistor
We can write: but this is Ohm’s law!
What can we elicit from this?
“ Two resistor R1, R2 between the same two points are equivalent to a single resistor RP which value is:
R1, R2 are named parallel resistors and RP is called equivalent resistor of R1 and R2.
“two or more resistors are in parallel configuration if they are connected between the same two points, as a consequence they have the same potential difference at the extremities”
If the parallel resistors are more than two (R1, R2, R3, ….) the equivalent resistor RP can be found as:
This means that in a circuit we can substitute 2 parallel resistors with the equivalent resistor simplifying the net.
The potential difference at the extremities doesn’t change but in the new circuit the currents through the two resistors disappear
Calculate VAB, VBC and VAC in the following circuit if the current I is equal to 2A (amps)
The current over R1 from A to B (IA->B) is equal to the current over R2 from B to C (IB->C) and is equal to I
With the Ohm’s law we can find
for the second Kirchhoff’s law
If we suppose to have a resistor we can write
And this is the Ohm’s law!
We can say that R1 and R2 are in series configuration and that Rs=R1+R2 is the equivalent resistor of the series configuration.
“two ore more resistors R1, R2, R3, … are in series configuration if the current through all of the resistors is the same.
In this case the resistors can be substitute with a single resistor which value is: “
When we use the equivalent series resistor the points between the resistors disappear but the current through the resistor doesn’t change.
Calculate the currents I1, I2, I3 and the potential difference VAB and VBC in the following circuit
Using the simplified circuits, we can calculate all the currents and the potential differences in the circuit.
Let’s start with the simplest circuit where we find
Using I4 in the second one you can find
Using VDA in the third one we find I1 and I4
At the and with I1 and I5 we can calculate
from 9500 Ω to 10500Ω
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The currents I2 and I3disappear
First of all, we have to reduce the circuit replacing the two parallel resistors (R2 and R3)
with the parallel equivalent resistor R23:
Where R23 is
and finally we replace R1 and R23 with the series equivalent resistor R123
The point in-between B disappear
with I1 we find VAB and VBC in circuit B
Now we can calculate I1 with Ohm’s law in circuit C
with VBC we obtain I2 and I3 in circuit A