1

DIRECT‐CURRENT CIRCUITS

BASIC CONCEPTS

Resistors in circuits.

Kirchhoff’s Rules

Ammeters and Voltmeters

R‐C Circuits

2

In Chapter 24 we found equivalent

capacitance for combinations of capacitors.

3

4

For resistors we need similar equations.

The current I through each R is same.

The voltage

And

5

Therefore

Can replace the three resistors with one

resistor with resistance

6

The total current I is divided between

7

And

Therefore

Or

For Parallel.

8

Consider the following circuit.

What is the current through the 6 Ω

resistor?

12V

9

ΩΩ

Therefore there are 6A through the 1Ω

resistor.

Ω

The emf of the battery is

Ω

The current through the resistor is

Ω

10

Example:

1.25A

What does the voltmeter read?

11

KIRCHHOFF’S RULES

Junction Rule

The sum of the currents into a junction is

zero.

12

Loop Rule

The sum of the potential differences in a

loop is zero.

13

Sign Convention

For resistors:

For batteries:

14

Example:

Loop 1 (start at a)

Loop 2 (start at c)

I1

I2

IR

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Loop 3 (start at a)

Junction a

Junction b

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R‐C CIRCUITS

No current.

17

Then close switch.

Apply Kirchhoff’s Loop Rule.

Across resistor potential change

Across battery potential change

Across capacitor potential change

18

Start at a.

The current is

Put in equation.

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The charge on the capacitor goes from 0 to

Q. Start the stopwatch when the switch is

closed and time goes from 0 to t.

Integrate

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The charge on the capacitor increases

exponentially with time.

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Charge on capacitor:

Current in circuit:

23

And

Define

Current starts and decreases

24

25

EXALMPLE: Consider this circuit:

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Find:

a. The time constant

b. The maximum charge on C

c. The time for the charge to reach 99%

of .

d. The current when

e.

f. Q when

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DISCHARGING CAPACITOR

After long time capacitor has charge .

Connect points a and c.

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Now capacitor discharges through the

resistor and:

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Integrate from while

Then