# Level 3 Physics: Demonstrate understanding of electrical systems Batteries and Kirchoff s Laws - Answers

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1 Level 3 Physics: Demonstrate understanding of electrical systems Batteries and Kirchoff s Laws - Answers In 03, AS 956 replaced AS The Mess that is NCEA Assessment Schedules. In AS 9053 there was an Evidence column with the correct answer and Achieved, Merit and Excellence columns explaining the required level of performance to get that grade. Each part of the question (row in the Assessment Schedule) contributed a single grade in either Criteria (Explain stuff) or Criteria (Solve stuff). From 003 to 008, the NCEA shaded columns that were not relevant to that question (Sorry haven t had time to do 004 yet). In 956, from 03 onwards, each part of a question contributes to the overall Grade Score Marking of the question and there are no longer separate criteria. There is no shading anymore. There is no spoon. At least their equation editor has stopped displaying random characters over the units. BTW there has not been a question on batteries and Kirchoff s laws since 04 (even though it s in the standard) Question Evidence Achievement Merit Excellence 04() I 0I 5.0I.7I = I = 0 Kirchhoff equation attempted. Total resistance is 30. Ω. Complete correct working (ignore negative value). I = = A Total PD is.0 V.

2 The current will flow right to left (anticlockwise), because the +ve terminal of the V battery is at a higher potential than the +ve terminal of the 0V battery, and current flows from high potential to lower potential. Right to left / anticlockwise because the top battery has a higher potential difference. Right to left/ anticlockwise because positive calculated value is produced when clockwise current is used. The current will flow right to left (anticlockwise), because, when a Kirchhoff equation is constructed with the current flowing in this direction, the value of the current is positive. (c) If I is the current through switch, I the current through switch, and I 3 the current through switch 3: I =.486 A I = A I +I =I 3 (S +S =S 3) I and I correctly calculated and added. I 3 = I + I.0 5.0I.7I = 0 I = I.5 I = 0 I = I 3 =.873 =.87 A

3 (d) The emf of the battery will stay the same, but the internal resistance will increase. The resistance of branch will increase, so the current will decrease. As the current through the 0.0 resistor decreases, the voltage through the resistor will decrease. The power delivered to the resistor will drop because of the drop in voltage and current. The emf of the battery will stay the same. The current will decrease. Lost volts increases. Output Voltage decreases. Power decreases. Attempt at calculating change in P/ Vo/ I Power will decrease, because current and output voltage will decrease. Power decreases because output voltage/ current decreases but emf constant. Power decreases because lost volts increases. Calculation using P = I R, no mention about emf or V 0 Output P decreases because more power is used by internal resistance. A decrease in power will occur because current and voltage will decrease, because the resistance of branch has increased, while the emf has stayed the same. Correct calculations comparing before and after. 0() =.4 W Accept.3.5 Correct answer.4 Ω (c) 7.4 V A best fit line drawn through the points crosses the y-axis at 7.4 V. This shows that when there is no current the terminal potential would be 7.4 V. When there is no current through the internal resistance, the terminal potential will equal the EMF of the cell. Gradient: ma -00 ma = -.4 W Kirchoff s law says IR = ε Ir so the gradient is the negative of the internal resistance. Accept V. Correct answer referring to the graph trend line and linking EMF to no current or no-load voltage..4 Ω..4 Ω AND Statement that gradient is the internal resistance.

4 (d) New line drawn so that the y-intercept is the same, but the gradient is steeper. The EMF of the cell will remain the same over time but the internal resistance of the cell will increase (as the products of the reaction in the cells build up). Correct intercept. Steeper gradient. Wrong line, but statement that internal resistance has increased. Correct line. Correct line and complete reasoning. Internal resistance has increased and the EMF remains same 0() I = V R = 4 + =.00 A Note: No working required. (i) I B + I N = I C I B + I N I C = 0 (ii) For out side loop I B 4 = I B = A Demonstrates concept knowledge of voltage law. Any loop equation correctly written Correct I B or correct application of the voltage law but wrong answer I C = = 5.7 A for RHS loop: ( ) I C = 0.44 = I C I C = 5.7 A

5 008() EMF/ Electro motive force / Open circuit voltage Correct R = V I = Correct working. (c) Correct R tot. Correct working showing all steps (formula not required). (d) If a battery with a higher internal resistance was used: There is a greater drop in pd across the internal resistance, so the pd is reduced across the lamp, so less current flows, so bulb is less bright / has less power. Dimmer lamp/lower voltmeter reading/lower terminal voltage/greater total resistance/lower current. Dimmer lamp due to less current / lower terminal pd. Complete explanation with voltage or current argument. The circuit has a greater total resistance, so less current flows, so bulb is less bright / has less power.

6 (e) Two identical lamps in parallel have half the resistance Correct calc of R for bulbs. Correct answer (consistent with answer to (c)). 007().50.0I 0 5I = 0 I = = = 0.06 A Note.0Ω resistor needed Correct answer (f) I = I + I 3 Correct equation

7 (g) This is a SHOW question V = Ir Watch for.48608v (if used I=.06A) or current calculated in b (N) Correct working. V = I is zero I = I 3 = I.50 ( ) I = 0 I = V T = = V (N) (=.4909V) V= (+5) (I = ) V = = V= ( + 5) =.4909 V before rounding (h) V terminal.64 V C = = V C = 0.85 V Care with 0.86V (N) I = (=.64 5 ) gives V bulb = = V

8 005() This is a show question Bottom and top lines correct Equivalent statement The battery has a much lower internal resistance than the solar cell and so a much higher current can be drawn. The terminal voltage of both the battery and the cell are the same so the battery can deliver far more power than the cell. ONE correct and relevant statement: Typical responses might be: Lower internal resistance Total resistance (in circuit) is reduced Higher current (drawn from battery). Watch for contradictory statements. Voltage across (supplied to) motor will be greater Battery will deliver more power Link made between the lower internal resistance or total resistance and the higher current lower internal resistance, higher voltage across motor or terminal or circuit or similar lower internal resistance and greater power (to drive the motor). Link made between the lower internal resistance and the higher current. AND higher voltage (across motor). Terminal voltages the same AND current increased. Terminal voltages (of solar cell and battery) the same From data given terminal voltage is 7.4V. (c) Around any closed loop or circuit, the sum of or total or adding the voltages are equal to zero or equivalent statement. Correct statement.

9 (d) From the outside loop:

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Data Sheet for Series and Parallel Circuits Name: Partner s Name: Date: _ Period/Block: _ Build the two circuits below using two AAA or AA cells. Measure and record Voltage (Volts), Current (A), and Resistance

### Searching for Patterns in Series and Parallel Circuits

Searching for Patterns in Series and Parallel Circuits Use the Circuit Construction Kit on phet.colorado.edu (DC Circuits only) to build the following circuits. fter building each circuit, use the ammeter