Question

Each of the four circuits in the drawing consists of a single resistor whose resistance is either R or 2R, and a single battery whose voltage is either V or 2V. The unit of voltage in each circuit is V = 10 V and the unit of resistance is R = 8

. Determine (a) the power supplied to each resistor and (b) the current delivered to each resistor.

Answer 1

To determine the power supplied to each resistor and the current delivered to each resistor in the given circuits, you can use the formulas P = (V^2) / R and I = V / R. By substituting the values of resistance and voltage for each circuit, it is possible to calculate the power and current. Circuits 1 and 2 have a power of 12.5W and 25W, and a current of 1.25A. Circuits 3 and 4 have a power of 6.25W and 50W, and a current of 0.625A and 2.5A, respectively.

Step-by-step explanation:

In order to determine the power supplied to each resistor and the current delivered to each resistor in the given circuits, we need to consider the different combinations of resistance and voltage in each circuit. Let's examine each circuit one by one.

Circuit 1:

Assuming V = 10V and R = 8Ω, the resistance of the single resistor is R = 8Ω and the voltage of the battery is V = 10V. Thus, the power supplied to the resistor is determined by the formula P = (V^2) / R, where V is the voltage across the resistor and R is the resistance. Substituting the values, we get P = (10^2) / 8 = 12.5W. The current delivered to the resistor can be calculated using Ohm's Law, which states that I = V / R. Substituting the values, we get I = 10V / 8Ω = 1.25A.

Circuit 2:

Assuming V = 10V and R = 8Ω, the resistance of the single resistor is 2R = 16Ω and the voltage of the battery is 2V = 20V. Using the same formulas as above, we can calculate that the power supplied to the resistor is P = (20^2) / 16 = 25W and the current delivered to the resistor is I = 20V / 16Ω = 1.25A.

Circuit 3:

Assuming V = 10V and R = 8Ω, the resistance of the single resistor is 2R = 16Ω and the voltage of the battery is V = 10V. Using the same formulas as above, we can calculate that the power supplied to the resistor is P = (10^2) / 16 = 6.25W and the current delivered to the resistor is I = 10V / 16Ω = 0.625A.

Circuit 4:

Assuming V = 10V and R = 8Ω, the resistance of the single resistor is R = 8Ω and the voltage of the battery is 2V = 20V. Using the same formulas as above, we can calculate that the power supplied to the resistor is P = (20^2) / 8 = 50W and the current delivered to the resistor is I = 20V / 8Ω = 2.5A.