In the circuits shown above, a battery with a voltage ?V bat = 9 V is connected
ID: 1301636 • Letter: I
Question
In the circuits shown above, a battery with a voltage ?Vbat = 9 V is connected to the circuit with resistances R1 = R2 = 25 ohms, unknown resistor R3, and a switch connected to R3.
The volt meter measures the potential difference between the points A and B, ?VAB.
Define ?VO be the reading on the voltmeter when the switch is open and ?VC be the reading on the voltmeter when the switch is closed.
If the ratio (?VC / ?VO) = 0.30, what is the value of the resistance of R3?
Give your answer in ohms to three signficant digits.
Please show work. Thank you!
Explanation / Answer
Delta V0:
Current in the circuit = 9/ ( 25 + 25) = 0.18 A
delta V0 = 0.18 * 25 = 4.5 V
Delta Vc = 0.3 * delta V0 = 0.3 * 4.5 = 1.35 V
Current in circuit = (9 - 1.35 )/ 25 = 0.306 A
Current through R2 = 1.35 / 25 = 0.054 A
Current through R3 = 0.306 - 0.054 = 0.252 A
R3 = 1.35 / 0.252 = 5.35714285714 ohms