Week 10 Day 1 Concept Question Bulbs and Batteries in Parallel Correct answer 1 An ideal battery is hooked to a light bulb with wires A second identical light bulb is connected in parallel to the rst light bulb After the second light bulb is connect the current from the battery compared to when only one bulb was connected is higher Inside Battery non zero chemical force f inside battery zero outside moves charges through a region in which static electric eld E opposes motion Ideal battery net force on charges is zero Potential difference between its terminals Extend path through external circuit where f is zero Symbols for Circuit Elements Electromotive Force EMF Battery Resistor R Capacitor C Inductor L Switch S The work per unit change around a closed path is called electromotive force EMF This is a bad name because it is not a force Let f denote the force per unit charge then the EMF is If a conducting closed path is represented then Ideal Battery EMF Sum of Potential Differences around a Closed Path Reference System for Circuit Analysis Sum of potential differences across all elements around any closed circuit loop must be zero Simplify resistors in series and in parallel Assign current and current direction in each branch Assign circulation direction for each loop Circulation direction across each element de nes before and after side of element De ne electric potential difference across a circuit element by V V after V before V a V b Sign Convention Battery Sign Convention Resistor Internal Resistance Circulating from the negative to positive terminal of a battery increases your potential Circulating from the positive to negative terminal of a battery decreases your potential Direction of current is the same as direction of electric eld which points to lower electric potential Circulating across a resistor in the direction of current decreases the potential Circulating across a resistor in the opposite direction of current increases the potential Real batteries have an internal resistance r which is small but non zero Terminal voltage V V b V a Ir The same current I must ow through both resistors Equivalent resistance Resistors in Series Current Conservation Sum of currents entering any junction in a circuit must equal su of currents leaving that junction Resistors in Parallel Voltage drop across the resistors must be the same Equivalent resistance Concept Question Resistors in Parallel Correct Answer 1 Suppose that R R Then the equivalent resistance is Group Problem Four Resistors Four resistors are connected to a battery as shown in the gure The current in the battery is I the battery emf is and the resistor values are R R R 2R R 4R R 3R Determine the current in each resistor in terms of I Measuring Potential Difference Measuring Current 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 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 Concept Question Measuring Current Correct answer 4 If R R compare the currents measure by the three ammeters Measuring Resistance An ohmmeter must be hooked in parallel across the element you want to measure the resistance of a resistor Ohmmeters apply a voltage and measure the current that ows They typically won t work if the resistor is powered connected to a battery Concept Question Bulbs and Batteries in Series Correct answer 2 An ideal battery is hooked to a light bulb with wires A second identical light bulb is connected in series with the rst light bulb after the second light bulb is connected the current from the battery compared to when only one bulb was connected is lower Power is change in energy per unit time So power to move current through circuit elements P I V Moving from the negative to positive terminal of a battery increases your potential If current ows in that direction the battery supplies power P I Moving across a resistor in the direction of current decreases your potential Resistors always dissipate power P I V I R V R Electrical Power Power Battery Power Resistor Joule Heating Concept Question Power in Parallel Concept Question Power in Series Correct answer 2 An ideal battery is hooked to a light bulb with wires A second identical light bulb is connected in parallel to the rst light bulb After the second light bulb is connected the power output from the battery compared to when only one bulb was connected is twice as high Correct answer 5 An ideal battery is hooked to a light bulb with wires A second identical light bulb is connected in series with the rst light bulb After the second light bulb is connected the light power from the rst bulb compared to when only one bulb was connected is a quarter as much Sum of Potential Differences around a Closed Path Sum of potential differences across all elements around any closed circuit loop must be zero 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 gure When Rvar is adjusted to 12 ohms there is zero current through the ammeter What is the unknown resistance Ru
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