Asked by Desiree LeBoeuf on May 10, 2024
Verified
A series RC circuit contains two resistors and two capacitors. The resistors are 82 Ω and 47 Ω . The capacitors have capacitive reactances of 80 Ω and 50 Ω . What is the total impedance?
A) 14.56 Ω
B) 68.62 Ω
C) 84.75 Ω
D) 183.14 Ω
Total Impedance
The overall resistance to the flow of alternating current in a circuit, combining the effects of resistance, inductive reactance, and capacitive reactance.
Capacitive Reactances
The resistance a capacitor offers to alternating current, depending on the frequency of the current and the capacitance.
Series RC
A circuit configuration where a resistor and a capacitor are connected sequentially in a single path for current to flow.
- Determine total impedance in a series RC circuit with multiple resistors and capacitors.
Verified Answer
KB
Karyn BurrowMay 11, 2024
Final Answer :
D
Explanation :
The total impedance in a series RC circuit is found by first summing the resistances and the capacitive reactances separately and then combining them using the Pythagorean theorem. The total resistance is 82Ω+47Ω=129Ω82 \Omega + 47 \Omega = 129 \Omega82Ω+47Ω=129Ω , and the total capacitive reactance is 80Ω+50Ω=130Ω80 \Omega + 50 \Omega = 130 \Omega80Ω+50Ω=130Ω . The total impedance ZZZ is then 1292+1302=16641+16900=33541≈183.14Ω\sqrt{129^2 + 130^2} = \sqrt{16641 + 16900} = \sqrt{33541} \approx 183.14 \Omega1292+1302=16641+16900=33541≈183.14Ω .
Learning Objectives
- Determine total impedance in a series RC circuit with multiple resistors and capacitors.