Answer:
Z = 1879.64 Ω = 1.879 KΩ
Explanation:
First, we will find the capacitive reactance of the capacitor:
[tex]X_{c} = \frac{1}{2\pi fc}\\[/tex]
where,
Xc = Capacitive Reactance = ?
f = frequency = 50 Hz
C = Capacitance = 2 μF = 2 x 10⁻⁶ F
Therefore,
[tex]X_{c} = \frac{1}{2\pi(50\ Hz)(2\ x\ 10^{-6} F)}\\X_{c} = 1591.55\ \Omega[/tex]
This is an RC series circuit. In the RC circuit the value of impedance is given by the following formula:
[tex]Z = \sqrt{R^2 + X_{c}^2}\\Z = \sqrt{(1000\ \Omega)^2 + (1591.55\ \Omega)^2}\\[/tex]
Z = 1879.64 Ω = 1.879 KΩ
