For a combined circuit: parallel and series a. Compare the total resistance expe

Question

For a combined circuit: parallel and series

a. Compare the total resistance experienced by the potential difference and current through the battery (i.e. the net resistance) to that for the three resistors when combined according to the rules in your textbook/lecture notes.

b. Explain what happens to the current as it leaves the resistor (R1) connected to the positive terminal of the power supply.

c. If you were to make a complete loop through the power supply, first resistor and second resistor, what would be your total potential change?

d. If you were to make a complete loop through the power supply, first resistor and third resistor, what would be your total potential change?

e. Do Kirchhoff’s rules hold in all of your circuits? Why or why not?

How would your conclusions apply to a voltage difference applied across (a part) of the human body?

Discuss the validity of Kirchhoff’s rules. Do they always apply? If so, why? If not, when do they apply?

Give the largest (or two largest) sources of uncertainty in you measurements. How would you change this?

Circuit Element I (A) R (S2) Battery ( Voltage 6.716 025 801.2 Source) R1 R2 R3 1.739 1.739 3.238 007 009 009 248.2 193.2 359.8

Explanation / Answer

Solution:

When the resistances are connected in series, total (net) resistance= R = R1+R2+R3

=> R = 248.2 + 193.2 + 359.8 = 801.2 ohms

When they are connected in parallel, net resistance = R = [1/R1+1/R2+1/R3]-1

=> R = [ 1/248.2 + 1/193.2 + 1/359.8 ] -1= 83.4 ohms

b) Observe that the net resistance is far less when they are connected in parallel. So the current thru the circuit will be higher in parallel , than when connected in series.

c) Total potential change when the 1st and 2nd resistor are connected in parallel = V = R! I =R2 I

=(248.2) (0.007) = 1.74 V

d) When the 1st and 3rd are connected in series, the potential diffenece = V1 = I1R1 = (0.007)(248.2) = 1.737 V

   V3 = I3 R3 = (0.009)(359.8) = 3.238 V

Total potential change = V1 +V3 = 1.737 + 3.238 = 4.976 V

d) Kirchoff's laws are valid only if the loop ( circuit) does not have a fluctuating magnetic field.

So it is not valid for High -frequency AC circuits.

Another assumption made is that the current starting at one end of the loop reaches the other end. This is NOT a safe assumption in high frequency AC circuits.

Sources of error (uncertainity):

1) The variation in the temperature of the resistances and

2) The internal resistance of the battery .

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