current conservation, power and fundamental circuits review: i = σa v/d = v / r where a is a cross...

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Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage across the wire. We call the quantity characterizing the material conductivity σ. Inverse of σ is called resistivity ρ, ρ = 1/σ

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Page 1: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Current conservation, power and fundamental circuits

Review:

I = σA V/d = V / R

where A is a cross section area of a wire, d is length. V is the voltage across the wire. We call the quantity characterizing the material conductivity σ.

Inverse of σ is called resistivity ρ, ρ = 1/σ

R= ρ d/A

Page 2: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Resistance• Valid for “ohmic” devices mainly metallic

conductors at constant temperature.

Page 3: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Conservation of current

Page 4: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Q3. What is the magnitude of the current flowing through the conductor at the bottom?

Page 5: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Circuit elements

Elements with negligible resistance---Wires.

We assume that there is no potential difference across a wire.

Page 6: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Electrical Hazards

Electrical Hazards

Feel: 1mApain: few mAdeadly: over 70mA

Page 7: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Electrical Power

• P = VQ/t = VI

• Unit: Watt (W) = VA

• kW, MW, GW

Page 8: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Electrical power on the ohmic device

• P = VI

• V = RI (Ohm’s Law)

• P = V2/R = I2R

Page 9: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Q2. The 60 W bulb is working at 120V. What is the current flowing

through the bulb?

Page 10: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Q3. The 60 W bulb is working at 120V. What is the resistance of the

bulb (in ohms)?

Page 11: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Fuses and switch

Page 12: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Q4. The voltage across the nail is 2V at 25A. What is the resistance of the nail

(in Ohms)?

Page 13: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Q5. The voltage across the nail is 2V at 25A. What is the power dissipated in

the nail?

Page 14: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Kirchhoff's rules

• At any junction point, the sum of all currents entering the junction must equal the sum of all currents leaving the junction.

( Conservation of charge)

• The Sum of the changes in potential around any closed path of the circuit must be zero

Page 15: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Page 16: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Combinations of resistors• Resistors in series:

• V = V1+V2+V3 = IR1+ IR2+ IR3

• Req = V/I = R1+ R2+ R3

V

R1 R2 R3

Page 17: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Combinations of resistors• Resistors in parallel

• I = I1+I2+I3 = V/ R1 + V/ R2+ V/R3

• I = V/Req

• 1/Req = 1/ R1+ 1/ R2+ 1/R3

R3

V

R2

R1

Page 18: Current conservation, power and fundamental circuits Review: I = σA V/d = V / R where A is a cross section area of a wire, d is length. V is the voltage

Combinations of resistors• Resistors in parallel

• 1/Req = 1/ R1+ 1/ R2+ 1/R3

• Req = R1∙R2∙R3 / (R1∙R2 + R2∙R3 + R1∙R3)

• Notice Req is smaller than all of them!

R3

V

R2

R1

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