Current = charges in motion Electric Current Current = charges in motion Magnitude rate at which net positive charges move across a cross sectional surface Units: [I] = C/s = A (ampere) J = current density (vector) in A/m² Current is a scalar, signed quantity, whose sign corresponds to the direction of motion of net positive charges by convention

Ohm’s Law constant R Ohm’s Law Power dissipation : R V R I Resistance (definition) constant R Ohm’s Law Power dissipation :

EMF – Electromotive Force An EMF device is a charge pump that can maintain a potential difference across two terminals by doing work on the charges when necessary. Examples: battery, fuel cell, electric generator, solar cell, fuel cell, thermopile, … Converts energy (chemical, mechanical, solar, thermal, …) into electrical energy. Within the EMF device, positive charges are lifted from lower to higher potential. If work dW is required to lift charge dq, EMF

Resistors in Series The current through devices in series is always the same. Req i ε R1 R2 i ε For multiple resistors in series: Same equation for parallel connected capacitors

Real Battery = Resistors in Series The current through devices in series is always the same. Req i ε terminal voltage internal resistance Show the demo of old battery before and after closing the switch.

Resistors in Parallel Same equation for capacitors connected in serial Devices in parallel has the same potential drop Generally, Same equation for capacitors connected in serial

Kirchhoff’s Rules Kirchhoff’s Rule 1: Loop Rule When any closed loop is traversed completely in a circuit, the algebraic sum of the changes in potential is equal to zero. Coulomb force is conservative Kirchhoff’s Rule 2: Junction Rule The sum of currents entering any junction in a circuit is equal to the sum of currents leaving that junction. Conservation of charge In and Out branches Assign Ii to each branch

Circuit Analysis Tips Simplify using equivalent resistors Label currents with arbitary directions If the calculated current is negative, the real direction is opposite to the one defined by you. Apply Junction Rule to all the labeled currents. Useful when having multiple loops in a circuit. Choose independent loops and define loop direction Imaging your following the loop and it’s direction to walk around the circuit. Use Loop Rule for each single loop If current I direction across a resistor R is the same as the loop direction, potential drop across R is ∆V = −I×R, otherwise, ∆V = I×R For a device, e.g. battery or capacitor, rely on the direction of the electric field in the device and the loop direction to determine the Potential drop across the device Solve simultaneous linear equations Current dirction is the moving direction of positive charge, i.e. the electric field direction, therefore, following the current direction, potential drops

Loop Example with Two EMF Devices Þ If 1 <2, we have I<0 !? This just means the actual current flows reverse to the assumed direction. No problem!

Finding Potential and Power in a Circuit But what is I? Must solve for I first! supplied by 12V battery Just means 0 V here Current dirction is the moving direction of positive charge, i.e. the electric field direction, therefore, following the current direction, potential drops dissipated by resistors The rest? into 4V battery (charging)

Charging a Battery Positive terminal to positive terminal Charging EMF > EMF of charged device battery being charged (11V) good battery (12V) Say, R+r1+r2=0.05 (R is for jumper cables). Then, power into battery 2 If connected backward, Large amount of gas produced Huge power dissipation in wires

Using Kirchhoff’s Laws in Multiple Loop Circuits Identify nodes and use Junction Rule: Identify independent loops and use Loop Rule: Only two are independent.

Warm-up quiz (a). 2.0A (b). 1.0A (c). -2.0A (d). -1.0A I1+I2 I2 What’s the current I1 ? I1 (a). 2.0A (b). 1.0A (c). -2.0A (d). -1.0A (e). Need more information to calculate the value.

Answer for the Warm-up quiz I1+I2 I2 Sketch the diagram Simplify using equivalent resistors Label currents with directions Use Junction Rule in labeling Choose independent loops Use Loop Rule Solve simultaneous linear equations I1 Replace by equivalent R=2 first.

Ammeter and Voltmeter Ammeter: an instrument used to measure currents It must be connected in series. The internal resistance of an ammeter must be kept as small as possible. Voltmeter: an instrument used to measure potential differences It must be connected in parallel. The internal resistance of a voltmeter must be made as large as possible.

Galvanometer Inside Ammeter and Voltmeter Galvanometer: a device that detects small currents and indicates its magnitude. Its own resistance Rg is small for not disturbing what is being measured. shunt resistor galvanometer Ammeter: an instrument used to measure currents Voltmeter: an instrument used to measure potential differences galvanometer

What is the current through R1 ? PHYS241 – Quiz 11A What is the current through R1 ? 30 30 0.575A 0.5A 0.75A 0.33A 1.5A R1 R2 45V 45V R3 30

What is the current through R2 ? PHYS241 – Quiz11B What is the current through R2 ? 10 10 0.33A 2.5A 0.75A 1.5A 0.5A R1 R2 15V 15V R3 10

What is the current through R3 ? PHYS241 – Quiz 11C What is the current through R3 ? 20 20 0.375A 0.5A 0.75A 1A 1.5A R1 R2 30V 30V R3 20