In the circuits shown above, a battery with a wattage Delta V bat = 12 V is conn

Question

In the circuits shown above, a battery with a wattage Delta V bat = 12 V is connected to the circuit with resistances R1 = R2 = 45 ohms, unknown resistor R3, and a switch connected to R3. The volt meter measures the potential difference between the points A and B, Delta V ab Define DeltaV0 be the reading on the voltmeter when the switch is open and Delta VC be the reading on the voltmeter when the switch is closed. If the ratio (DeltaV0 / Delta Vq) = 0.80, what is the value of the resistance of R3? Give your answer in ohms to three significant digits. Do not include units in your answer.

Explanation / Answer

delta V0:

Current through Circuit = 12/ ( 45 + 45) = 0.133 A

Delta V0 = 0.133 * 45 = 6 V

Delta Vc = 6 / 0.8 = 7.5 V

Currrent through circuit = (12 - 7.5 ) / 45 = 0.1 A

Current through R2 = 7.5 / 45 = 0.167 A

Current through R3 = 0.167 - 0.1 = 0.067A

R3 = 7.5 / 0.067 = 111.940298507 = 111.940 ohms

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