The power P delivered to each resistor is the product of the current squared (I^

Question

The power P delivered to each resistor is the product of the current squared (I^2) and the corresponding resistance R, or P = I^2*R. The resistances are known, and Ohm's law can be used to find the current. Ohm's law states that the current in the circuit (which is also the current through each of the resistors) equals the voltage V of the battery divided by the equivalent resistance Rs of the two resistors: I = V/Rs. Since the resistors are connected in series, we can obtain the equivalent resistance by adding the resistances.

Three resistors, 3 O, 4.5 O, and 5.5 O, are connected in series across a 12-V battery. Find the power delivered to each resistor.

Explanation / Answer

The three resistors are in series, so the sum of them is an equivalent resistor. 3 + 4.5 + 5.5 = 13 Ohms And being connected to a 12 V battery allows you to use Ohm's law : V = IR, or I = V/R Use I = V/R To find the Current through the resistors! I = (12V) / (13 Ohm) = .923077 A Power delivered to each resistor is P = (I^2)(R), and since the resistors are in series, each resistor has the same current running through them. So to find the power delivered to each resistor, just multiply the current by each individual resistor. For Resistor 3: P = (.923077A)^2 * (3 Ohm) = 2.556 Watts For Resistor 4.5: P = (.923077A)^2 * (4.5 Ohm) = 3.834 Watts For Resistor 5.5: P = (.923077A)^2 * (5.5 Ohm) = 4.686 Watts

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