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DC Circuits. Series and parallel rules for resistors Kirchhoff’s circuit rules . “DC” Circuits. “ Direct Current or DC ”: current always flows in one direction. For circuits containing only resistors and emf’s the current is always constant in time. Circuits containing

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Dc circuits
DC Circuits

  • Series and parallel rules for resistors

  • Kirchhoff’s circuit rules


Dc circuits1
“DC” Circuits

“Direct Current or DC”: current always flows in one direction.

For circuits containing only resistors and emf’s the

current is always constant in time. Circuits containing

other elements such as capacitors and inductors as

well as resistors will have currents that change with

time.

Alternating current or AC is current that reverses

direction many times (eg: 60 Hz current in Canada) and

will not be treated in this course


Resistors in series
Resistors in Series

R1

R2

R3

I

B

A

We want to replace this combination by a single

resistor with resistance Reff

I

A

B

Reff


  • Same current through all resistors

  • Voltages add:

  • Veff = V1 + V2 + V3 + …

  • IReff = IR1 + IR2 + IR3+ … (same current through all)

So,

Easy way to remember: think of the length of a string:

Ltot = L1 + L2 + L3 where L1 etc are the segments


Resistors in parallel
Resistors in Parallel

I

A

I1

I2

I3

R1

R2

R3

B

I

We want to replace these resistors by a single

resistance Reff:

A

I

Reff

B


Example: find the effective resistance of resistors

of 5  and 10  in series and parallel.


Example 1

R1

R3

11 V

R2

R6

R4

R5

Example 1

All resistors = 1 Ω

Find: Effective resistance across the battery


Example 2

R

R

R

R

R

R

Example 2

Find the effectiveresistance of a network of identical resistors


Example 3

a

3 Ω

18 V

b

Example 3

Find a) the current in each resistor

b) the power dissipated by each resistor

c) the equivalent resistance of the three resistors


Example 4
Example 4

A regular “40 watt” bulb and a “60 watt” bulb are connected in SERIES across 120 V.

What power does each bulb give? (Assume that the resistances don’t change with temperature—these are special bulbs.)


Kirchhoff s circuit rules
Kirchhoff’s Circuit Rules

Junction Rule: total current in = total current out

at each junction (from conservation of charge).

Loop Rule: Sum of potential differences around any closed loop is zero (from conservation of energy).

Charge q moves through circuit changing its potential

energy qV but eventually there is no overall change.


I2

I1

I3

Junction Rule: conservation of charge.

I1 = I2 + I3

Sum of currents entering a junction equals the sum of

currents leaving the junction

Alternately:

I2

I1

I1 = I2 + (I1-I2)

I1-I2


Loop Rule: conservation of energy.

Follow a test charge q around a loop:

 around any loop in circuit.

R

I

ΔV = -IR

-

+

ΔV =

ΔV = Q/C

-Q

+Q

C

loop

loop going from left to right


Example 5
Example 5

c

200Ω

300 Ω

a

b

12 V

300 Ω

400Ω

d

a) What is Vab when the switch is open?

b) Find the current through the switch when it is closed.



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