In the circuit shown, the battery has an EMF (voltage) of 31 V, the two resistan
ID: 1342769 • Letter: I
Question
In the circuit shown, the battery has an EMF (voltage) of 31 V, the two resistances, r, each have a resistance r = 3 ?, and R1 = 45 ?. If the voltage across R1 is 19 V, what is the resistance of R2?
Assume all resistances are shown, so there is no need to consider other internal resistances such as those due to the battery or wires.
Give your answer in Ohms to three signficant digits.
Please show some work, there are variations of this problem that have a negative answer but I don't know if this one does or not.
Explanation / Answer
Let I is the current through battery and r
Apply KVL in the right loop,
EMF - I*r - 17 - I*r = 0
2*I*r = EMF - 17
I = (31 - 17)/(2*3)
= 2.33 A
we know,
current through R2, I2 = I - I1
= 2.33 - 17/R1
= 2.33 - 17/45
= 1.956 A
I2 = I*R1/(R1 + R2)
R1 + R2 = I*R1/I2
R2 = I*R1/I2 - R1
= 2.33*45/1.956 - 45
= 8.604 ohms <<<<<<<<<<<----------------Answer