Week 04, Day 2 W10D2 DC Circuits Today’s Reading Assignment W10D2 DC Circuits & Kirchhoff’s Loop Rules Course Notes: Sections 7.1-7.5 1 Class 09 1

Announcements PS 8 due Week 11 Tuesday at 9 pm in boxes outside 32-082 or 26-152 Next Reading Assignment W10D3 PS07: PhET: Building a Circuit 7.1-7.5, 7.10 Exam 3 Thursday April 18 7:30 pm –9:30 pm Class 12

Outline DC Circuits Kirchoff’s Laws Electrical Power Measuring Voltage and Current Class 12

DC Circuits Class 12

Examples of Circuits Class 12

Symbols for Circuit Elements Battery Resistor Capacitor Switch Equipotential Junction Branch Class 12

Electromotive Force (EMF) The work per unit charge around a closed path done is called electromotive force EMF. This is a bad name because it is not a force. Let denote the force per unit charge, then the EMF is If a conducting closed path is present then Class 22

Ideal Battery Inside Battery: chemical force , non-zero inside battery (zero outside), moves charges through a region in which static electric field opposes motion 2) Ideal battery: net force on charges is zero 3) Potential difference between its terminals 4) Extend path through external circuit where Class 12

Concept Question The electric field inside the battery points to The left The Right Class 12

Concept Question Answer The electric field inside the battery points to The left Goes from positive to negative charge Class 12

Sign Conventions - Battery Moving from the negative to positive terminal of a battery increases your potential Moving from the positive to negative terminal of a battery decreases your potential Class 12

Concept Question The electric field inside the resistor points to The left The Right Class 12

Concept Question Answer The electric field inside the resistor points to The right Electric field pushes charge in the same direction, so current in direction of E This is cause and effect! Class 12

Sign Conventions - Resistor Moving across a resistor in the direction of current decreases your potential Direction of current Is the same as direction of electric field which points to lower electric potential Moving across a resistor in the direction of current decreases your potential Class 12

Internal Resistance Real batteries have an internal resistance, r, which is small but non-zero Terminal voltage: (Even if you short the leads you don’t get infinite current) Class 12

Series vs. Parallel Series Parallel Class 12

Resistors In Series The same current I must flow through both resistors Class 12

Current Conservation Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction. Class 14

Resistors In Parallel Voltage drop across the resistors must be the same Class 12

Concept Q: Resistors In Parallel Suppose that . Then the equivalent resistance 2. 3. 4. Class 12

Concept Q: Resistors In Parallel Answer 1. When Then the equivalent resistance is the smaller resistance. This is an important circuit design principle. Class 12

Group Problem: Four Resistors Four resistors are connected to a battery as shown in the figure. The current in the battery is I, the battery emf is ε, and the resistor values are R1 = R, R2 = 2R, R3 = 4R, R4 = 3R. Determine the current in each resistor in terms of I. Class 14

Measuring Voltage & Current Class 14

Measuring Potential Difference A voltmeter must be hooked in parallel across the element you want to measure the potential difference across Voltmeters have a very large resistance, so that they don’t affect the circuit too much Class 14

Measuring Current An ammeter must be hooked in series with the element you want to measure the current through Ammeters have a very low resistance, so that they don’t affect the circuit too much Class 14

Concept Question: Measuring Current If R1 > R2, compare the currents measured by the three ammeters: I1 > I2 > I3 I2 > I1 > I3 I3 > I1 > I2 I3 > I2 > I1 I3 > I1 = I2 None of the above Not enough information is given. Class 14

Concept Question Answer: Measuring Current Answer: 4. I3 > I2 > I1 The total current must add to the two individual currents, so I3 must be largest. Most current prefers to go through the smaller resistor so I2 > I1 . Class 14

Measuring Resistance An ohmmeter must be hooked in parallel across the element you want to measure the resistance of Here we are measuring R1 Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery) Class 14

Concept Question: Bulbs & Batteries An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in parallel to the first light bulb. After the second light bulb is connected, the current from the battery compared to when only one bulb was connected. Is Higher Is Lower Is The Same Don’t know Class 12

Concept Question Answer: Bulbs & Batteries Answer: 1. More current flows from the battery There are several ways to see this: (A) The equivalent resistance of the two light bulbs in parallel is half that of one of the bulbs, and since the resistance is lower the current is higher, for a given voltage. (B) The battery must keep two resistances at the same potential  I doubles. Class 12

Concept Question: Bulbs & Batteries An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in series with the first light bulb. After the second light bulb is connected, the current from the battery compared to when only one bulb was connected. Is Higher Is Lower Is The Same Class 12

Concept Question Answer: Bulbs & Batteries Answer: 2. Less current flows from the battery The equivalent resistance of the two light bulbs in series is twice that of one of the bulbs, and since the resistance is higher the current is lower, for the given voltage. Class 12

Electrical Power Power is change in energy per unit time So power to move current through circuit elements: Class 14

Power - Battery Moving from the negative to positive terminal of a battery increases your potential. If current flows in that direction the battery supplies power I Class 14

Power – Resistor (Joule Heating) Moving across a resistor in the direction of current decreases your potential. Resistors always dissipate power Class 14

Concept Question: Power An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in parallel to the first light bulb. After the second light bulb is connected, the power output from the battery (compared to when only one bulb was connected) Is four times higher Is twice as high Is the same Is half as much Is ¼ as much Class 14

Concept Question Answer: Power Answer: 2. Is twice as high The current from the battery must double (it must raise two light bulbs to the same voltage difference) and Class 14

Concept Question: Power An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in series with the first light bulb. After the second light bulb is connected, the light (power) from the first bulb (compared to when only one bulb was connected) Is four times higher Is twice as high Is the same Is half as much Is ¼ as much Class 14

Concept Question Answer: Power Answer: 5. Is 1/4 as bright R doubles  current is cut in half. So power delivered by the battery is half what it was. But that power is further divided between two bulbs now. Class 14

Kirchhoff’s Loop Rules Class 14

Recall: Current Conservation Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction. Class 14

Sum of Potential Differences Around a Closed Path Sum of potential differences across all elements around any closed circuit loop must be zero. Class 12

Sum of Potential Differences Around a Closed Path Sum of potential differences across all elements around any closed circuit loop must be zero. Class 12

Demonstration: Five Different Types of Resistance F13 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=F 13&show=0 Class 14

Steps of Solving Circuit Problem 1. Straighten out circuit (make squares) 2. Simplify resistors in series/parallel 3. Assign current loops (arbitrary) 4. Write loop equations (1 per loop) 5. Solve Class 14

Worked Example: Circuit What is current through each branch of the circuit shown in the figure below? Class 14

Worked Example: Simple Circuit Current conservation at a: Lower Loop: Start at a and circulate clockwise. Then Upper Loop: Start at a and circulate counterclockwise. Then Solve for I2: and Class 14

Demonstration: Wheatstone Bridge F14 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=F 14&show=0 Class 14

Group Problem: Wheatstone Bridge A circuit consisting of two resistors with R1=6.0 ohms and R2=1.5 ohms, a variable resistor, with resistance Rvar, a resistor of unknown value Ru, and 9.0 volt battery, are connected as shown in the figure. When Rvar is adjusted to 12 ohms, there is zero current through the ammeter. What is the unknown resistance Ru? Class 14