A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm and released from rest. In the electrical analog the maximum charge on the capacitor is 0.25 C.The maximum current in the LC circuit is
To determine the maximum current in an LC circuit, we will need to use some formulas from electromagnetism.
Firstly, it is important to understand the behavior of an LC circuit. An LC circuit consists of an inductor (L) and a capacitor (C) connected in parallel. When the circuit is energized, the capacitor stores electrical energy, and the inductor stores magnetic energy. The energy oscillates back and forth between the two components, resulting in an oscillating current.
The formula we will be using to determine the maximum current is:
Imax = Vmax / sqrt(L * C)
Where:
Imax is the maximum current in the circuit,
Vmax is the maximum voltage across the capacitor,
L is the inductance of the inductor, and
C is the capacitance of the capacitor.
Since we are given the maximum charge on the capacitor (0.25 C) instead of the maximum voltage, we need to convert the charge to voltage using the formula:
Vmax = Qmax / C
Where:
Qmax is the maximum charge on the capacitor,
C is the capacitance of the capacitor.
However, before we proceed, we need to determine the values of L and C based on the information provided in the question.
From the given information, we know the mass (m) of the block (150 g) and the displacement (x) of the block (25 cm). We can use these values to calculate the potential energy stored in the spring using the formula:
U = (1/2)kx^2
Where:
U is the potential energy stored in the spring,
k is the spring constant, and
x is the displacement of the block.
The potential energy stored in the spring is equal to the energy stored in the capacitor, as they are analogous in this electrical system.
U = (1/2)kx^2
U = (1/2) * 35 N/m * (0.25 m)^2
Now that we have the potential energy of the spring, we can equate it to the energy stored in the capacitor (U = (1/2)CV^2) to find the capacitance (C) of the capacitor.
(1/2)CV^2 = U
C * (0.25 C)^2 = (1/2) * 35 N/m * (0.25 m)^2
Once we determine the capacitance (C), we can substitute it into the formula for maximum current (Imax = Vmax / sqrt(L * C)) and solve for Imax.