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An in-depth explanation of resistors in series and parallel circuits, including how to identify series and parallel connections, calculate currents and voltages, and apply Kirchhoff's Rules. It covers the concepts of equivalent resistance, current splitting, and voltage drops in series and parallel combinations.
What you will learn
Typology: Slides
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Today’s agenda:
Resistors in Series and Parallel. You must be able to calculate currents and voltages in circuit components in series and in parallel.
Kirchoff’s Rules. You must be able to use Kirchoff’s Rules to calculate currents and voltages in circuit components that are not simply in series or in parallel.
Recall from lecture 7:
Series:
Circuit elements can be connected neither in series nor in parallel.
A (^) B
Parallel: (^) A B
In contrast:
A B
If you ever have a choice of which wire to follow when moving from A to B, the circuit elements are not in series.
If each element provides an alternative path between the same points A and B, the elements are in parallel.
Circuit elements can be connected neither in series nor in parallel.
Are these resistors in series or parallel?
Not enough information: It matters where you put the source of emf.
+ -
V
parallel
+ -
V
Current: same current flows through all resistors (conservation of charge: all charge entering the series of resistors at A must leave it at B)
Voltage: voltages in a series add up VAB=V 1 +V 2 +V 3 (loop rule, see last lecture, reflecting conservation of energy)
A (^) B
V = IReq
IR 1 + IR 2 + IR 3 = IReq
R 1 + R 2 + R 3 = Req
A B
Req
Replace the series combination by a single “equivalent” resistor (producing same total voltage for same current)
+ -
V
Current:
A B
Voltage:
+ -
V
A B^ **V
A (^) B
Req
Replace parallel combination by single equivalent resistor
1 2 3
eq
eq 1 2 3
Dividing both sides by V gives
eq 1 2 3
Summary:
Series A^ B^ eq i i
same I, V’s add
Parallel A^ B
same V, I’s add
eq i i
Let’s discuss the strategy!
Example: calculate the equivalent resistance of the resistor “ladder” shown. All resistors have the same resistance R.
