The Lead Acid Electric Battery + - Spongy Lead (Pb) Lead Oxide (PbO 2 ) Sulfuric Acid Solution H 2 SO 4 Sulfuric Acid Electrolyte: Oxidation at the Negative Plate (Electrode:Anode): Reduction at the Positive Plate (Electrode:Cathode): I Terminals Cell: 2 V Battery: Multiple cells

Batteries

Kirchoff’s Rules Conservation of charge Junction (Node) Rule: At any junction point, the sum of all currents entering the junction must equal the sum of the currents leaving the junction. Conservation of energy Loop Rule: The some of the changes in potential around any closed path of a circuit must be zero.

Energy in a circuit

Series Circuit + Apply the Loop Rule

Parallel Circuits + Apply the Junction Rule

Rule Set – Problem Solving Strategy A resistor transversed in the direction of assumed current is a negative voltage (potential drop) A resistors transversed in the opposite direction of assumed current is a positive voltage (potential rise) A battery transversed from – to + is a positive voltage. A battery transversed from + to - is a negative voltage. Ohm’s Law applies for resistors. Both the loop rule and junction rule are normally required to solve problems.

More about the Loop Rule Traveling around the loop from a to b In (a), the resistor is traversed in the direction of the current, the potential across the resistor is – IR In (b), the resistor is traversed in the direction opposite of the current, the potential across the resistor is is + IR

Loop Rule, final In (c), the source of emf is traversed in the direction of the emf (from – to +), and the change in the electric potential is +ε In (d), the source of emf is traversed in the direction opposite of the emf (from + to -), and the change in the electric potential is -ε

Example Problem 1 Given: Find: current in each resistor V = 3 Volts

Example Problem 2 Given: Find: current in the 20  resistor

Alternating Current

AC Power ?

Root Mean Square (rms)

The Wheatstone bridge a simple Ohmmeter

Charging a capacitor in an RC circuit At t = 0, Q o = 0 and Same Symbol

Solving the charging differential equation Kirchoff’s loop rule Convert to a simple equation in Current by taking the first derivative w.r.t. time Separate variables

Integrate the results

Charge buildup

Discharging the capacitor in an RC circuit At t = 0, Q = Q o

Solving the discharging differential equation Kirchoff’s loop rule Separate variables Integrate

Charge and current decay

Electrical Safety Current kills, not voltage (70 mA) Normal body resistance = 10 5  But could be less than 1000  Take advantage of insulators, remove conductors Work with one hand at a time Shipboard is more dangerous Electrical safety is an officer responsibility