Series/Parallel Combination Circuit 3
Solution:
a) Determine the total resistance of the circuit (including the internal resistance). (3 marks)
Given that the circuit is a series/parallel combination, we must first determine the resistance of the parallel section separately and then add its value to the other resistors which are in series with the parallel part. Note that in the third branch of the parallel part the 13 W and 8.0 W resistor are in series within that branch, thus the resistance of the third branch is 21 W.
Thus the total resistance of the circuit is given by
b) Determine the total current in the circuit. (2 marks)
Given that the power dissipated by the internal resistor is 10W and that the value of the internal resistor is 1.5W, the total current in the circuit can be calculated using the formula P = I^{2}R. Note that all the current in the circuit must necessarily go through the battery and thus the internal resistor.
Thus the total current in the circuit is given by
c) Determine the voltage drop across the internal resistor. (2 marks)
Given that we now know the current through r, the voltage drop can easily be determined using Ohm's Law.
d) Determine the voltage drop across the 7.0 W resistor. (6 marks)
Given that the voltage drop across all branches of a parallel circuit are equal, and that the equivalent resistance of the parallel branches is 3.0 W, the voltage drop can once again be calculated using Ohm's Law.
e) Determine the voltage drop across the 13 W resistor. (3 marks)
Given that the voltage drop across all branches of a parallel circuit are equal, and that the resistance of the third branch is 21 W, the current in that branch can be calculated using Ohm's Law.
This current must flow through both the 8.0W resistor and the 13 W resistor. The voltage drop across the 13 W resistor can be calculated using Ohm's Law.
f) Determine the emf of the battery. (4 marks)
If we consider the circuit as one with an ideal battery (i.e. no internal resistance) then the emf can simply be viewed as the total voltage of the circuit. Again, Ohm's Law is used to calculate this value.
We could also use the formula , however we must first determine the terminal voltage V_{t}. Recognizing that the terminal voltage would be equivalent to the sum of the voltage drops outside of the battery, and that the resistance of the circuit outside of the battery is 8.0 W, (5.0 W + 3.0 W) , we can calculate V_{t} using Ohm's Law.
Thus the emf can be given by
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