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.

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Presentation transcript:

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

Resistance Valid for “ohmic” devices mainly metallic conductors at constant temperature.

Conservation of current

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

Circuit elements Elements with negligible resistance---Wires. We assume that there is no potential difference across a wire.

Electrical Hazards Feel: 1mA pain: few mA deadly: over 70mA

Electrical Power P = VQ/t = VI Unit: Watt (W) = VA kW, MW, GW

Electrical power on the ohmic device P = VI V = RI (Ohm’s Law) P = V 2 /R = I 2 R

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

Q3. The 60 W bulb is working at 120V. What is the resistance of the bulb (in ohms)?

Fuses and switch

Q4. The voltage across the nail is 2V at 25A. What is the resistance of the nail (in Ohms)?

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

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

Combinations of resistors Resistors in series: V = V 1 +V 2 +V 3 = IR 1 + IR 2 + IR 3 R eq = V/I = R 1 + R 2 + R 3 V R1R1 R2R2 R3R3

Combinations of resistors Resistors in parallel I = I 1 +I 2 +I 3 = V/ R 1 + V/ R 2 + V/R 3 I = V/R eq 1/R eq = 1/ R 1 + 1/ R 2 + 1/R 3 R3R3 V R2R2 R1R1

Combinations of resistors Resistors in parallel 1/R eq = 1/ R 1 + 1/ R 2 + 1/R 3 R eq = R 1 ∙R 2 ∙R 3 / (R 1 ∙R 2 + R 2 ∙R 3 + R 1 ∙R 3 ) Notice R eq is smaller than all of them! R3R3 V R2R2 R1R1