In a circuit with a 12V power supply, a 220Ω resistor, and a 470μF capacitor, calculate the power dissipated in the resistor and the power stored in the capacitor when the circuit reaches steady-state after charging.
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To calculate the power dissipated in the resistor, we need to calculate the current flowing through it first. We can use Ohm's law to do this:
V = IR
where V is the voltage across the resistor, I is the current flowing through it, and R is the resistance. Rearranging the equation gives us:
I = V / R
Plugging in the values, we get:
I = 12V / 220Ω = 0.0545A
Now that we have the current, we can calculate the power dissipated in the resistor using the formula:
P = IV
where P is power and V is voltage. Plugging in the values, we get:
P = 0.0545A * 12V = 0.654W
So the power dissipated in the resistor is 0.654W.
To calculate the power stored in the capacitor, we use the formula:
P = 0.5 * CV^2
where P is power, C is the capacitance, and V is the voltage across the capacitor. Plugging in the values, we get:
P = 0.5 * 470μF * (12V)^2 = 0.033W
So the power stored in the capacitor is 0.033W.
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