In an AC circuit, if the voltage is given by V(t) = V₀ sin(ωt), what is the expr

₹0.0

Question: In an AC circuit, if the voltage is given by V(t) = V₀ sin(ωt), what is the expression for the current through a capacitor? (2022)

Options:

Correct Answer: I(t) = C dV/dt

Exam Year: 2022

Solution:

The current through a capacitor is given by I(t) = C dV/dt. For V(t) = V₀ sin(ωt), the current can be derived from this expression.

In an AC circuit, if the voltage is given by V(t) = V₀ sin(ωt), what is the expression for the current through a capacitor? (2022)

In an AC circuit, if the voltage is given by V(t) = V₀ sin(ωt), what is the expression for the current through a capacitor? (2022)

Step 1: Identify the voltage function given in the problem, which is V(t) = V₀ sin(ωt).
Step 2: Recall the formula for current through a capacitor, which is I(t) = C dV/dt.
Step 3: Differentiate the voltage function V(t) with respect to time t to find dV/dt.
Step 4: Calculate dV/dt: dV/dt = d/dt [V₀ sin(ωt)] = V₀ ω cos(ωt).
Step 5: Substitute dV/dt back into the current formula: I(t) = C (V₀ ω cos(ωt)).
Step 6: Simplify the expression to get the final result: I(t) = C V₀ ω cos(ωt).

Capacitor Current Relationship – The relationship between voltage and current in a capacitor, where current is the derivative of voltage with respect to time multiplied by capacitance.
AC Circuit Analysis – Understanding how alternating current (AC) behaves in circuits, particularly with reactive components like capacitors.
Differentiation in AC Functions – Applying calculus to find the rate of change of sinusoidal functions, which is essential for determining current from voltage.