The current in the oscillatory circuit depends on time as I

In an oscillatory circuit, the current depends on time and can be represented by the equation I = Imsinωt, where Im = 9.0 mA, and ω = 4.5*10^4 s^-1. The capacitance of the capacitor is C = 0.50 µF. It is necessary to find the inductance of the circuit and the voltage across the capacitor at time t = 0.

To solve the problem, we use the formula for the resonant frequency of the oscillatory circuit: ω0 = 1/(LC)^0.5, where L is the inductance of the circuit, and C is its capacitance. Solving the equation for ω0, we find the inductance value: L = 1/(Cω0^2) = 2.22 mH.

The voltage across the capacitor at time t = 0 can be found by substituting t = 0 into the equation for the current I = Imsinωt and using the formula for the voltage across the capacitor U = Q/C, where Q is the charge on the capacitor. Thus, at time t = 0, the voltage on the capacitor will be equal to U = Im/(ωC) = 4 V.

Current in the oscillatory circuit

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This product is a description of a physics problem related to an oscillatory circuit.

The problem states that the current in the oscillatory circuit depends on time as I = Imsinωt, where Im = 9.0 mA, ω = 4.5*10^4 s^-1. Capacitor capacity C = 0.50 µF.

It is necessary to find the inductance of the circuit and the voltage across the capacitor at time t = 0.

To solve this problem, use the formula for the resonant frequency of the oscillatory circuit:

ω0 = 1/√(LC)

where L is the inductance of the circuit, C is the capacitance of the capacitor, ω0 is the resonant frequency.

From this formula we can express the inductance of the circuit:

L = 1/(Cω0^2)

To find the voltage across the capacitor at time t = 0, use the formula:

UC = q/C

where q is the charge on the capacitor.

The charge on a capacitor can be expressed in terms of current:

q = ICt

At time t = 0, the charge on the capacitor is zero, so the voltage across the capacitor at time t = 0 is zero.

So, the inductance of the circuit is equal to:

L = 1/(Cω0^2) = 2,0 Гн

The voltage across the capacitor at time t = 0 is zero.

Thus, we found the required values ​​- the inductance of the circuit and the voltage on the capacitor at time t = 0.

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