Reference Directions, Voltage and Current Measurements and Power


Here are two example circuits that illustrate the importance of voltage and current reference directions. You can change the resistance using the scrollbar. Also, left-clicking the mouse on either meter will reverse the red and black probes.



Consider the circuit on the left. In this circuit, the voltage across the resistor is equal to the voltage of the voltage source, 24 V, as shown. The power dissipated by the resistor can be calculated as

The ammeter measures the current in the resistor. I1 is the current that is directed left to right through the ammeter and then downward through the resistor. I1and the resistor voltage, 24 V, shown in the figure, adhere to the passive convention. Therefore, the power dissipated by the resistor can also be calculated as

In contrast, I2 is the current that is directed right to left through the ammeter and upward through the resistor. To see I2, left-click the mouse on the ammeter to reverse the red and black probes of the ammeter, changing the reference direction of the current measured by the ammeter. (The ammeter measures the current directed form the red probe toward the black probe.) I2 is similar to, but not equal to I1. I2 and the resistor voltage, 24 V, shown in the figure, do not adhere to the passive convention. Therefore, the power calculated as

is the power supplied by the resistor instead of the power dissipated by the resistor.

In summary,


Next, consider the circuit on the right. In this circuit, the current in the resistor is equal to the current of the current source, 2A, as shown. The power dissipated by the resistor can be calculated as

The voltmeter measures the voltage across the resistor. V1 is the voltage with the + above the -. V1and the resistor current, 2 A, shown in the figure, adhere to the passive convention. Therefore, the power dissipated by the resistor can also be calculated as

In contrast, V2 is the voltage with the - above the +. To see V2, left-click the mouse on the voltmeter to reverse the red and black probes of the ammeter, changing the reference direction of the voltage measured by the voltmeter. (The voltmeter measures the voltage with + at the red probe and - at the black probe.) V2 is similar to, but not equal to V1. V2and the resistor current, 2 A, shown in the figure, do not adhere to the passive convention. Therefore, the power calculated as

is the power supplied by the resistor instead of the power dissipated by the resistor.

In summary,



Challenges:

    Adjust the resistance to 36 ohms.

    1. Calculate the power dissipated by the resistor in the circuit on the left from the resistor voltage and the resistance.

    2. Calculate the power dissipated by the resistor in the circuit on the left from the resistor voltage and the resistor current.

    3. Confirm that the values calculated in a and b are equal.

    4. Calculate the power dissipated by the resistor in the circuit on the right from the resistor current and the resistance.

    5. Calculate the power dissipated by the resistor in the circuit on the right from the resistor voltage and the resistor current.

    6. Confirm that the values calculated in d and e are equal.

  1. Adjust the resistance so that resistor in the circuit on the left dissipates 9 W. (Hint: .)

    1. Calculate the power dissipated by the resistor in the circuit on the left from the resistor voltage and the resistance.

    2. Calculate the power dissipated by the resistor in the circuit on the left from the resistor voltage and the resistor current.

    3. Confirm that the values calculated in a and b are equal.

    4. Calculate the power dissipated by the resistor in the circuit on the right from the resistor current and the resistance.

    5. Calculate the power dissipated by the resistor in the circuit on the right from the resistor voltage and the resistor current.

    6. Confirm that the values calculated in d and e are equal.

  2. Adjust the resistance so that resistor in the circuit on the right dissipates 16 W.

    1. Calculate the power dissipated by the resistor in the circuit on the left from the resistor voltage and the resistance.

    2. Calculate the power dissipated by the resistor in the circuit on the left from the resistor voltage and the resistor current.

    3. Confirm that the values calculated in a and b are equal.

    4. Calculate the power dissipated by the resistor in the circuit on the right from the resistor current and the resistance.

    5. Calculate the power dissipated by the resistor in the circuit on the right from the resistor voltage and the resistor current.

    6. Confirm that the values calculated in d and e are equal.