To find the current in the wire, we can use Ohm's Law, which states that I = V/R, where I is the current, V is the voltage, and R is the resistance. The resistance of the wire can be found using the formula R = ρL/A, where ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area of the wire.
First, we need to convert the thickness of the wire from millimeters to meters:
1 mm = 0.001 m
Next, we can calculate the cross-sectional area of the wire:
A = πr^2 = π(0.0005 m)^2 = 7.85 x 10^-7 m^2
Now we can find the resistance of the wire:
R = ρL/A = (1.69 x 10^-8 Ω⋅m)(0.3 m)/7.85 x 10^-7 m^2 = 6.48 Ω
Finally, we can use Ohm's Law to find the current:
I = V/R = 1 V/6.48 Ω = 0.154 A
Therefore, the current in the wire is 0.154 A.
To find the total impedance of the circuit, we can use the formula Z = √(R^2 + Xc^2), where R is the resistance of the resistor and Xc is the reactance of the capacitor, which is given by Xc = 1/(2πfC), where f is the frequency of the emf and C is the capacitance of the capacitor.
Since the circuit is in series, the total impedance is simply the sum of the resistance and reactance:
Z = R + Xc
We can find the reactance using the given values:
Xc = 1/(2πfC) = 1/(2π(60 Hz)(1 μF)) = 2.65 kΩ
Now we can find the total impedance:
Z = R + Xc = 1000 kΩ + 2.65 kΩ = 1002.65 kΩ
The current in the circuit can be found using Ohm's Law:
I = V/Z = 120 V/1002.65 kΩ = 0.119 A
Therefore, the current in the circuit is 0.119 A