Question

What is the impedance of a series combination of a 50-Ω resistor, a 5.0-μF capacitor, and a 10-μF capacitor at a frequency of 2.0 kHz?

Answer 1

Answer:

55.92 ohm

Explanation:

R = resistance of the resistor = 50 ohm

f = frequency = 2000 Hz

$C_{1}$ = Capacitance of first capacitor = 5.0 x 10⁻⁶ F

$C_{2}$ = Capacitance of second capacitor = 10 x 10⁻⁶ F

$C_{s}$ = Series combination of capacitance

Series combination of capacitance is given as

$C_{s} = \frac{C_{1}C_{2}}{C_{1} + C_{2}}$

$C_{s} = \frac{(5\times 10^{-6})(10\times 10^{-6})}{(5\times 10^{-6}) + (10\times 10^{-6})}$

$C_{s} = 3.33\times 10^{-6}$

$X_{c}$ = capacitive reactance of series combination

Capacitive reactance of capacitor is given as

$X_{c} = \frac{1}{2\pi f C_{s}$

$X_{c} = \frac{1}{2(3.14)(2000)(3.33\times 10^{-6})}$

$X_{c} = 23.91$ ohm

R = resistance of the resistor = 50 Ω

z = impedance of the circuit

Impedance is given as

$z = \sqrt{R^{2} + X_{c}^{2}}$

$z = \sqrt{50^{2} + 23.91^{2}}$

$z = \sqrt{50^{2} + 23.91^{2}}$

z = 55.92 ohm