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Unformatted text preview: ﬂ Ql‘l_(§h§ﬂ; Electric Circuits
Ph 5112 Winter 95 The circuit we will study today is shown in the ﬁgure.
For our orientation I have marked some points with the
letters A through F. The four resistors have the values F E R1=SOOQ R2= 10009
R3 = 1000 (2 R4 = 1500 Q The goal is to answer the following questions R4
Find the total current, I, and the total resistance, R.
What is the voltage across R4 (V4) ? What is the current through R2 (12) ? — D A B C a
Solution 1: the experimental approach a Voltmeter is used to measure the voltage ( =Jpotential difference) between two points of an electric circuit. Question I : Where in our circuit would yen connect a voltmeter to measure the battery voltage? Measured voltage (V): a Amperemeter is used to measure the current through a circuit element. To connect an amperemeter you have to
break the circuit and insert the meter. Question 2: Where in our circuit would you measure the total current?
Measured current (1):
Question 3: Find the total resistance R: Question 4: Describe the measurement of V; the voltage across resistor R9 ) I 1 measured value: 4 Question 5: Describe the measurement 0%, the current through resistor R151 I
i measured value: Solution 2: the theoretical approach we need a few basic laws, rules and equations Ohm’s Law can be applied to each element of the circuit, for example V2 = 12 R2 We usually ignore the very small resistance of connecting wires. Consequently, every point on the same wire is at
the same voltage. Question 6: Which points (A - F) in our circuit are at the same voltage? Loop Rule (Kirchhoff)
energy is conserved which simple means that if you go around a in a complete circle, the net change is zero. For an electric circuit this means:
the sum of all voltage changes in a loop is zero mm W Question 7: Write down all voltage changes for the loop
Battery 3—] i—b from a to b
+ from b to a Resistor ——-|/\/V\J—- in current direction
I 9 against current direc. Question 8: What is the current 11 ? Just assign a direction If the value you calculate for this current is positive, you picked the right direction Ifthe
value comes out to be negative, you picked the wrong direction Junction Rule (Kirchhoff) ,
charge is conserved: What goes in must come out!
the sum of the currents at a junction is zero Question 9: Assign your current directions and write down the (current) equations for the junctions at B, C, D, E Resistors in Series: Question 10: Apply the Loop Rule to circuit a) Question I 1: Apply the Loop Rule to circuit b) Solve for R = Parallel Resistors: When-k l' °
\/ .L R R1 3 R '
+ I i V - A: Find the total Resistance Rm: R1 R4 Analyze the circuit and start with the innermost series or
parallel sub—Circuit. In our case, this is resistors R2 and R3 in
parallel. R3 What is the combined resistance R23? It helps to re-draw the diagram with the ﬁrst sub-circuit
replaced by the combined resistor (R23 in our case) What is the next element to process? R4 - 9
What IS R234 . R23 Here is the new diagram.
What is the total resistance? R234 B} Find the total current I: in: s C} Find V4, the voltage across R4: Apply Ohm’s law to R4: V4 = R4 I4
R4 is given so we only need 14. How does 1.; compare to 1234, the current through R234? V Rtot Find [2342 51:1 Find V4: V23: V33 :13 R23 Find V; and 12, the current through R2: ...
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