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Understanding Currents and Voltages in Series and Parallel Circuits, Slides of Construction

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

  • What is the difference between series and parallel combinations of resistors?
  • How do you identify series and parallel connections in a circuit?
  • What is Kirchhoff's Junction Rule and how is it used?
  • What is Kirchhoff's Loop Rule and how is it used?
  • How do you calculate currents and voltages in series and parallel circuits?

Typology: Slides

2021/2022

Uploaded on 09/12/2022

borich
borich 🇬🇧

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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.
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Download Understanding Currents and Voltages in Series and Parallel Circuits and more Slides Construction in PDF only on Docsity!

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.

Resistances in Circuits

Recall from lecture 7:

  • two simple ways to connect circuit elements

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

R 1 R 2 R 3

+ -

V

I

Current: same current flows through all resistors (conservation of charge: all charge entering the series of resistors at A must leave it at B)

V 1 V 2 V 3

Resistors in series

I

I

I

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

V = V 1 + V 2 + V 3

IR 1 + IR 2 + IR 3 = IReq

R 1 + R 2 + R 3 = Req

Equivalent resistance

R 1 R 2 R 3

+^ V -

V^ I

1 V 2 V 3

I

I

I

A B

Req

+^ V -

I

Replace the series combination by a single “equivalent” resistor (producing same total voltage for same current)

V = IR 1 + IR 2 + IR 3

V

V

V

R 3

R 2

R 1

+ -

V

Current:

  • current I splits into currents I 1 , I 2 , I (^3) I = I 1 + I 2 + I 3 (conservation of charge)

I 3

I 1

I 2

Resistors in parallel

I

A B

Voltage:

  • Voltage drops across all three resistors are identical VAB= V 1 = V 2 = V 3 (conservation of energy)

Equivalent resistance

V

V

V

R 3

R 2

R 1

+ -

V

I 3

I 1

I 2

I

A B^ **V

  • -**

A (^) B

I

Req

Replace parallel combination by single equivalent resistor

I = I 1 + I 2 + I 3

1 2 3

V V V

I = + +

R R R

eq

V

I =

R

eq 1 2 3

V V V V

R R R R

Dividing both sides by V gives

eq 1 2 3

R R R R

Summary:

Series A^ B^ eq i i

R = ∑R

same I, V’s add

Parallel A^ B

same V, I’s add

eq i i

R R

Let’s discuss the strategy!

A

B

Example: calculate the equivalent resistance of the resistor “ladder” shown. All resistors have the same resistance R.

A

B

Parallel

  • new color indicates an equivalent resistor made up of several original ones

A

B

Series

A

B

Series

A

B

All done!