Question 394: AC fundamentals

Question

In an LCR series a.c. circuit, the voltage across each of the components L, C and R is 60 V. The voltage across the LC combination is

Accepted Answer

An LCR series A.C. circuit consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series. The voltage across each of these components is denoted by $V_L$, $V_C$, and $V_R$ respectively. In this particular problem, it is given that the voltage across each component is 60V.
To find the voltage across the LC combination, we first need to understand how voltages add up in an LCR circuit. The key concept here is that the voltages across the inductor (L) and the capacitor (C) are 90 degrees out of phase with the voltage across the resistor (R).
In a series LCR circuit, the impedance due to the inductor (L) and capacitor (C) can be given by:
$$ Z_L = j\omega L  $$
$$ Z_C = \frac{-j}{\omega C} $$
where $j$ is the imaginary unit and $\omega$ is the angular frequency of the alternating current source.
Given that voltages are 60V each, we observe that $V_L$ leads the current by 90 degrees and $V_C$ lags the current by 90 degrees. Because $V_L$ and $V_C$ are 180 degrees out of phase, they are directly opposite to each other. Thus, $V_L$ and $V_C$ will cancel each other out if they are equal in magnitude.
Hence, when we place them in combination, the resultant voltage will be:
$$ V_{	ext{LC}} = V_L - V_C = 60V - 60V = 0V $$
So, the voltage across the LC combination is zero volts. Thus, the answer is:
Option C
: zero V

Answer

120 V

Answer

60 V

Answer

zero V

Answer

$$\frac{60}{\sqrt{3}}$$ V

AC fundamentals

In an LCR series a.c. circuit, the voltage across each of the components L, C and R is 60 V. The voltage across the LC combination is

Choose the correct answer: