Lesson 6

Lesson 6Lesson 6

Direct Current CircuitsDirect Current Circuits

Electro Motive ForceElectro Motive ForceInternal ResistanceInternal ResistanceResistors in Series and ParallelResistors in Series and ParallelKirchoffs RulesKirchoffs Rules

RC CircuitsRC CircuitsCharging Charging Discharging CapacitorsDischarging CapacitorsElectrical InstrumentsElectrical Instruments

Galvanometer Galvanometer AmmeterAmmeterVoltmeterVoltmeterWheatstone BridgeWheatstone BridgePotentiometerPotentiometer

RC CircuitsRC CircuitsCharging Charging Discharging CapacitorsDischarging CapacitorsElectrical InstrumentsElectrical Instruments

Galvanometer Galvanometer AmmeterAmmeterVoltmeterVoltmeterWheatstone BridgeWheatstone BridgePotentiometerPotentiometer

Topics

Electro Motive Force (Electro Motive Force (emfemf))

Source of emf is any device that increases the

potential energy of charges circulating in a circuit.

Electric Potential increases by the emf E as

charge

goes from negative to positive plate of battery.

EMF I

EMF is

Work Done per unit charge by electrical pump

dWdQ

EMF II

Battery is a Charge PumpCurrent flowing internally in battery feels a resistance this is an Internal resistance, rFlowing positive charges (current) experience drop of electric potential in resistor

-

V=IR

R+

Charge Pump

- +- +

Terminals

Terminal Potential DifferenceV = E - Ir

+ -

Internal Resistance

Picture

Power and Internal Resistance

V Ir

V IR

IR Ir

I

R rThus power generated by emf

I 2

R r

Combination of ResistorsCombinations of Combinations of

Resistors Resistors

Parallelsame electric potential felt by each element

Serieselectric potential felt by the combination is the sum of the potentials across each element

SeriesV V1 V2 IR1 IR2

V I R1 R2 IReq

Req Ri

i

ParallelI I1 I2 V

R1

V

R2

I V1

R1

1

R2

V

Req

1Req

1R1

1R2

1

Req

1

Ri

i

Kirchoff’s RulesKirchoff’s Rules

The sum of the currents entering a junction must

equal the sum of the currents leaving

Conservation of Charge

Kirchoffs Rules I

The Sum of the Potential Differences around a

closed circuit loop must be zero

Conservation of Energy

Kirchoffs Rules II

Picture

RC circuits

RC CircuitsRC Circuits

Non Steady StateNon EquilibriumCurrent varies with time

Picture

When switch is closed

IR q

C0

Thus at time t = 0, q 0 0

I0 I 0 R

When capacitor is fully charged the current

in the circuit is zero and the charge on the capacitor is a max

Q qmax C

Charging I

Charging II

IR q

C 0

d

dt IR q

C

0 0 RdI

dt 1

C

dq

dt

RdI

dt I

C 0

dI

I 1

RCdt

dI

II 0

I

1

RCdt

0

t

ln

I

I 0

t

RC I t I 0 e

t

RC

I t R

e t

RC

Charging IIII t

R

e tRC

dq

dt

R

e

t

RC

dq R

e tRC dt

dq

0

q

R

e

t

RC dt

0

t

q t C 1 e

t

RC

Q 1 e

t

RC

Time ConstantTime Constant RC

R C VIQV

QQ

s

s

DischargingDischarging

+Q

-Q

IR qC

from Kirchoff

I dqdt the rate of decrease of charge

Discharging I

Discharging II

Rdqdt

qC

dq

q

1

RCdt

dq

qQ

q

1

RCdt

0

t

ln

q

Q

t

RC

q t Qe t

RC

I t dq

dt

Q

RCe

t

RC I0e t

RC