Statement of Kirchhoff’s Rules Junction Rule Junction Rule The sum of the currents entering any junction must equal the sum of the currents leaving that junctionThe sum of the currents entering any junction must equal the sum of the currents leaving that junction A statement of Conservation of Charge A statement of Conservation of Charge Loop Rule Loop Rule The sum of the potential differences across all the elements around any closed circuit loop must be zeroThe sum of the potential differences across all the elements around any closed circuit loop must be zero A statement of Conservation of Energy A statement of Conservation of Energy

Kirchoff’s Rules (1) Node rule, current law,.. I1I1 I2I2 I3I3 I 1 = I 2 + I 3 = +

R1R2 V R3 I V IR 1 IR 2 IR 3 V – IR 1 – IR 2 – IR 3 = 0 V = I (R 1 + R 2 + R 3 ) = I R eq

RECIPE (1) Indicate currents going through each circuit elements: * Realize that the same I flows through elements up to the junction points. * Make your best educated guess on the directions of I’s. (2) The currents are your unknowns. * You have to set up the same number of indep. Eqs. * At least one of them come from the I-law and the rest of them are from the V-law (3) Set up the appropriate loops and apply V-law for each loop. The direction of each loop can be either CW or CCW. * If the loop runs from (-) to (+) of a battery, the battery contributes (+) voltage (vice versa). * If the loop runs in the same direction as that of your current, the resistor contributes (-) voltage calculated from Ohm’s Law (vice versa). * Add all the contributions from the elements (R’s and batteries) in the loop will be set to “0”. 1 equation. ++ After all, if you get (-) current value, that simply means the current flows in the direction opposite to your guess.

5 3 6V 8 V I1 I2 I3 I1, I2, and I3 3 unknowns I 1 = I 2 + I 3 6 – 5*I 2 – 8 = *I 2 = 0I 2 = A 6 – 3*I 3 = 0I 3 = 2 A I 1 = 1.6 A This means that Your guess on the direction of I2 was wrong and actual current flows opposite direction.

Does Ohm’s law say this? Ohm: A liquid measure formerly used in Germany, varying locally between 30 and 36 gallons. With the same potential drop (voltage) applied, the larger current flows through the smaller resistance. With the same current flowing, larger potential drop develops across the larger resistance. If the resistance is infinite, no current flows regardless of potential (voltage) difference across the resistor. When there is no potential difference across an element, no current flows through regardless of the resistance. Yes, go check OED! Obvious! I = V/R Simple as V = IR

V4 V5 V I1 I2 I3 I 2 = I 1 + I 3 4 – 40I 1 – 3 – 10I 1 – 20I 2 = 01 – 50I 1 – 20I 2 = 0 4 – 50I 3 – 5 – 30I 3 – 20I 2 = 0-1 – 80I 3 – 20I 2 = 0 Example 21.3

Electrical Safety Electric shock can result in fatal burns Electric shock can result in fatal burns Electric shock can cause the muscles of vital organs (such as the heart) to malfunction Electric shock can cause the muscles of vital organs (such as the heart) to malfunction The degree of damage depends on The degree of damage depends on the magnitude of the currentthe magnitude of the current the length of time it actsthe length of time it acts the part of the body through which it passesthe part of the body through which it passes

Effects of Various Currents 5 mA or less 5 mA or less can cause a sensation of shockcan cause a sensation of shock generally little or no damagegenerally little or no damage 10 mA 10 mA hand muscles contracthand muscles contract may be unable to let go a of live wiremay be unable to let go a of live wire 100 mA 100 mA if passes through the body for 1 second or less, can be fatalif passes through the body for 1 second or less, can be fatal

Ground Wire Electrical equipment manufacturers use electrical cords that have a third wire, called a ground Electrical equipment manufacturers use electrical cords that have a third wire, called a ground Prevents shocks Prevents shocks

Electrostatics and DC Circuit Revisited C h a r g e c o m e s i n t w o f l a v o r s, ( + ) a n d ( - ) ! Hmm, they can repel each other! FIELD E = F/q F = qE Work, P.E. W = F.d = qE.d E - p o t e n t i a l V = W / q = E. d Prof. Ohm V = IR R = V/I I = V/R