Question

For an RC circuit, find an expression for the angular frequency at which V = 1/2E₀.

a) ω = 1/RC
b) ω = 2/RC
c) ω = 1/2RC
d) ω = 1/√2RC

Answer 1

For an RC circuit, the expression for the angular frequency at which V = 1/2E₀ is c) ω = 1/₂RC. (option c)

Step-by-step explanation:

In an RC circuit, the relationship between voltage (V) and angular frequency (ω) is given by the formula:

V = 1 / (1 + jωRC)

where j is the imaginary unit. To find the angular frequency at which V = 1/2E₀, substitute V = 1/2E₀ into the formula:

1 / (2E₀) = 1 / (1 + jωRC)

To solve for ω, multiply both sides by the denominator:

2E₀ = 1 / (1 + jωRC)

1 + jωRC = 1 / (2E₀)

jωRC = (1 - 2E₀) / (2E₀)

jω = (1 - 2E₀) / (2E₀RC)

ω = (1 - 2E₀) / (2E₀jRC)

Rationalizing the denominator by multiplying the numerator and denominator by -j gives:

ω = (2E₀ - 1) / (2E₀RCj)

Simplifying further:

ω = (1 - 2E₀) / (2E₀RCj)

Comparing this expression to the given options, the correct answer is c) ω = 1/₂RC.(option c)