Physics for Scientists and Engineers II, Summer Semester Lecture 9: June 10 th 2009 Physics for Scientists and Engineers II

Physics for Scientists and Engineers II, Summer Semester Direct Current (DC) Circuits Batteries: Have constant electric potential difference between terminals.  Current’s direction is constant / Direct Current (DC) Batteries are a source of “electromotive force (emf)” (is not really a force…but an electric potential difference.)  is the maximum possible voltage the battery can provide between it’s terminals. Batteries have an “internal resistance” r  The terminal voltage for a real battery is LESS than  as soon as a current flows.

Physics for Scientists and Engineers II, Summer Semester Internal Resistance of Batteries Batteries have an “internal resistance” r  The terminal voltage for a real battery is LESS than  as soon as a current flows. +- a b c d e f R Delivered by battery Delivered to R Delivered to r

Physics for Scientists and Engineers II, Summer Semester Resistors in Series The same current passes through all resistors that are connected in series. + - a R1R1 R2R2 b c

Physics for Scientists and Engineers II, Summer Semester Resistors in Parallel The potential difference across resistors that are connected in parallel is the same. + - a R1R1 b c R2R2 d Points c and d are called “junctions”: The current I splits up into I 1 and I 2 at point c. The currents I 1 and I 2 combine at point d into I again.

Physics for Scientists and Engineers II, Summer Semester Example  1.00  48.0  3.0  10.0  6.0  34.0  1)What is R eq of this circuit? 2)Determine the current through each resistor. 3)Determine the voltage drop across each resistor. 4)Determine the power dissipated in each resistor. 5)What happens to the current through the battery if a resistor is removed? (Discuss qualitatively for each R).

Physics for Scientists and Engineers II, Summer Semester Example : What is R eq of this circuit?  1.00  48.0  3.0  10.0  6.0  34.0 

Physics for Scientists and Engineers II, Summer Semester Example : What is R eq of this circuit?  48.0  34.0 

Physics for Scientists and Engineers II, Summer Semester Example : What is R eq of this circuit? 

Physics for Scientists and Engineers II, Summer Semester Example : What is R eq of this circuit? + -

Physics for Scientists and Engineers II, Summer Semester Example : What is the current through each resistor?  1.00  48.0  3.0  10.0  6.0  34.0 

Physics for Scientists and Engineers II, Summer Semester Example : Get voltage drop across R C and R d 

Physics for Scientists and Engineers II, Summer Semester Example : Get the branch currents  48.0  34.0  a b c

Physics for Scientists and Engineers II, Summer Semester Example: Get all the voltage drops  1.00  48.0  3.00  10.0  6.00  34.0 

Physics for Scientists and Engineers II, Summer Semester Example: Get all the powers dissipated  1.00  48.0  3.00  10.0  6.00  34.0 

Physics for Scientists and Engineers II, Summer Semester Kirchhoff’s Rules

Physics for Scientists and Engineers II, Summer Semester Kirchhoff’s Rules: More on Junction Rule Count incoming currents as positive and outgoing currents as negative.

Physics for Scientists and Engineers II, Summer Semester Kirchhoff’s Rules: More on Loop Rule + - Imagine traveling along the indicated loop in the given direction: Sum up all the electric potential changes along the closed loop. 1)The emf is traversed from the negative to the positive side:  V increases (count positive) 2)The resistor R 1 is traversed in the same direction as the current:  V drops (count negative) 3 The resistor R 2 is traversed in the same direction as the current:  V drops (count negative)

Physics for Scientists and Engineers II, Summer Semester Kirchhoff’s Rules: More on Loop Rule + - Imagine traveling along the indicated loop in the other direction: Sum up all the electric potential changes along the closed loop. 1)The emf is traversed from the positive to the negative side:  V decreases (count negative) 2)The resistor R 1 is traversed in the opposite direction as the current:  V drops (count positive) 3 The resistor R 2 is traversed in the opposite direction as the current:  V drops (count positive) This is the same equation as before, just multiplied by -1.

Physics for Scientists and Engineers II, Summer Semester Example with two batteries Notice: I indicated a direction of current, even though I do not know in which direction the current really flows here.

Physics for Scientists and Engineers II, Summer Semester Example with two batteries

Physics for Scientists and Engineers II, Summer Semester Example: Multiple branches and batteries Find the currents through the resistors.

Physics for Scientists and Engineers II, Summer Semester Step1: Identify junctions and indicate currents You can choose the current direction as you like. A B

Physics for Scientists and Engineers II, Summer Semester Step2: Write down junction rules A B

Physics for Scientists and Engineers II, Summer Semester Step3: Indicate loops and write loop rules A B Loop 1 Loop 2 Loop 3

Physics for Scientists and Engineers II, Summer Semester Step4: Look at all the independent equations:

Physics for Scientists and Engineers II, Summer Semester Step5: Solve for the unknowns

Physics for Scientists and Engineers II, Summer Semester ….and solve….

Physics for Scientists and Engineers II, Summer Semester Step6: Indicate actual current direction A B