Download Single Current Loop E Single Current Loop II

Single Current Loop
For the most simple circuits:
I
E
+
R
E
V
I= =
R R
Single Current Loop II
A current loop is a circuit with any number of elements in it that
are connected so that current can flow around the loop. We
compute such a loop by looking at the voltages across the devices,
the sum of all these voltages has to add up to zero.
Circuit Rules:
Loop Rule: The sum of the changes in potential encountered
going all the way around a circuit loop must be zero.
Resistance Rule: When a resistor is encountered moving around
the loop, the change in potential (“voltage drop”) is –iR. (moving in
the direction of the current, +iR moving opposite, where i>0).
EMF Rule: (battery rule) When an EMF device is encountered,
the change in potential is +E (moving in the direction of the EMF arrow, -E if
moving in the opposite direction.)
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Example Loop I
E1 + E2 + E3 − IR1 − IR2 − IR3 = 0
I
E1
E2
E3
Batteries in series:
+
Etot = E1 + E2 + E3 + ...
R1
Vtot = V1 + V2 + V3 + ...
+
R2
+
Resistors in series:
Rtot = R1 + R2 + R3 + ...
R3
N
Rtot = ∑ Ri
i =1
Multi-Loop Circuits
I2
I0
I1
+
V0
R1
I 0 = I1 + I 2 ⇒
R2
Junction Rule:
The total current into a junction
must equal the total current out of a
junction (= conservation of charge.)
V0 V0 V0
1
1
1
= +
⇒
= +
Req R1 R2
Req R1 R2
N
1
1
=∑
Req i =1 Ri
2
Multi-loop Circuits II
Multi loop circuits are solved by combining the loop rule and the
junction rule.
Often you can significantly simplify the task by first simplifying the
circuit, replacing parallel or series resistors with the equivalent
resistor.
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