In an AC circuit, if the voltage is given by V(t) = V_0 sin(ωt), what is the expression for the current through a resistor R?

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Q: In an AC circuit, if the voltage is given by V(t) = V_0 sin(ωt), what is the expression for the current through a resistor R?

Solution: For a resistor, the current is in phase with the voltage. Therefore, I(t) = V(t)/R = (V_0/R) sin(ωt).

Steps: 6

Step 1: Understand that in an AC circuit, voltage can change over time. Here, the voltage is given by the formula V(t) = V_0 sin(ωt).
Step 2: Recognize that V_0 is the maximum voltage, ω is the angular frequency, and t is time.
Step 3: Know that in a resistor, the current (I) is directly related to the voltage (V) by Ohm's Law, which states I = V/R.
Step 4: Substitute the expression for voltage into Ohm's Law. So, I(t) = V(t)/R = (V_0 sin(ωt))/R.
Step 5: Simplify the expression. This gives I(t) = (V_0/R) sin(ωt).
Step 6: Conclude that the current through the resistor is also a sine wave, just like the voltage, but scaled by the factor of 1/R.