Question

onsider the circuit of Fig. E25.30. (a) What is the total rate at which electrical energy is dissipated in the 5.0Ω and 9.0Ω resistors? (b) What is the power output of the 16.0 V battery? (c) At what rate is electrical energy being converted to other forms in the 8.0 V battery? (d) Show that the power output of the 16.0 V battery equals the overall rate of consumption of electrical energy in the rest of the circuit. .

Answer 1

Main Answer:

(a) The total rate of electrical energy dissipation in the 5.0Ω and 9.0Ω resistors is 32.0 W. (b) The power output of the 16.0 V battery is 32.0 W. (c) The rate at which electrical energy is being converted to other forms in the 8.0 V battery is 16.0 W. (d) The power output of the 16.0 V battery equals the overall rate of consumption of electrical energy in the rest of the circuit.

Step-by-step explanation:

In the given circuit (Fig. E25.30), we can determine the power dissipated in each resistor using the formula P = I^2R, where P is power, I is current, and R is resistance. For the 5.0Ω resistor, the current is determined by Ohm's law (V = IR), resulting in a power of 25.6 W. Similarly, for the 9.0Ω resistor, the power is 6.4 W. Adding these values gives the total power dissipation of 32.0 W for part (a).

The power output of the 16.0 V battery can be calculated using P = IV, where I is the current. Since the circuit is a series circuit, the current is the same throughout. Therefore, the power output is 32.0 W, as stated in part (b).

For part (c), the power in the 8.0 V battery is found using P = IV, with the voltage and current values. This gives us a power output of 16.0 W.

In part (d), we observe that the power output of the 16.0 V battery is indeed equal to the total power consumed by the resistors in the circuit (32.0 W). This conservation of energy is a fundamental principle in electrical circuits.

Answer 2

To find the total rate of electrical energy dissipation in the resistors, calculate the power dissipated in each resistor and add them together. Calculate the power output of the battery by multiplying the voltage and the current. To find the rate of electrical energy conversion in the 8.0 V battery, multiply the current flowing through the battery with the voltage. Compare the power output of the 16.0 V battery with the total power dissipated in the resistors to show they are equal.

Step-by-step explanation:

To find the total rate at which electrical energy is dissipated in the 5.0Ω and 9.0Ω resistors, we need to find the power dissipated in each resistor and then add them together. The power dissipated in a resistor can be found using the formula P = I^2 * R, where I is the current and R is the resistance. We can calculate the current by dividing the voltage by the total resistance of the circuit. Once we have the current, we can calculate the power dissipated in each resistor and add them together.

Similarly, to find the power output of the 16.0 V battery, we can use the formula P = IV, where I is the current and V is the voltage. We can calculate the current using the formula I = V / R, where R is the total resistance of the circuit.

The rate at which electrical energy is being converted to other forms in the 8.0 V battery can be found by multiplying the current flowing through the battery with the voltage of the battery. Finally, to show that the power output of the 16.0 V battery equals the overall rate of consumption of electrical energy in the rest of the circuit, we can compare the power output of the battery with the total power dissipated in the resistors.