The voltage (in volts) induced in a coil of wire is v = (2t + 1)0.5. The current in the coil is initially 0.3 amps, and the inductance is 5H. What is the equation for the current in the coil?
To find the equation for the current in the coil, we need to use Faraday's law of electromagnetic induction, which relates the induced voltage in a coil to the rate of change of the magnetic flux through the coil.
According to Faraday's law, the induced voltage in a coil is given by the equation:
v = -L * di/dt
Where:
- v is the induced voltage
- L is the inductance of the coil
- di/dt is the rate of change of current in the coil
In this case, the induced voltage is given by v = (2t + 1)^0.5, and the inductance is 5H. We need to find the equation for the current, di/dt.
Let's start by rearranging the equation:
v = -L * di/dt
di/dt = -v / L
Now, plug in the given values:
di/dt = -((2t + 1)^0.5) / 5
Therefore, the equation for the current in the coil is:
di/dt = -((2t + 1)^0.5) / 5