# V1 = 2V Calculate Voltage, Power in Circuit w/ Inductor at t=>0

• Engineering
• freezer
In summary, for the given circuit with an inductor of 1H and a resistor of 2 ohms, the current through the inductor is defined by i(t)=0 if t is less than 0, and i(t)=1-e^{-2t} if t is greater than or equal to 0. When t is greater than or equal to 0, the following can be found: a) VL(t) = 0V, b) Vr(t) = (1-exp(-2t))/2, c) V1(t) = 2V, and d) the power absorbed by the inductor is given by W = 0.5(1)(1-e^{-2t})^
freezer

## Homework Statement

For the circuit shown below, the current through the inductor is defined as follows:

$$i(t)=\begin{cases} 0 & \text{if } -\infty <t<0 \\ 1-e^{-2t}& \text{if } 0\leq t < \infty \end{cases}$$

L = 1H, R2 = 2 ohms

For t=> 0 find:

a) VL(t)
b) Vr(t)
c) V1(t)
d) Power absorbed by the inductor

## Homework Equations

$$i(t)=\frac{v}{R}(1-e^{-Rt/L})$$

## The Attempt at a Solution

As t goes to infinity, current goes to 1A and the inductor becomes a wire. So V1 = 2V

But i don't think this is what it is asking for.
From the relevant equation section, solving for V would leave only 2

W = 0.5Li^2

W = 0.5(1)(1-e^{-2t})^2

Vr = (1-exp(-2t))/2

Vl = 0V

Looks like it wants t→0 ... for very small times, the exponential term is approximately linear.

## What is the significance of V1 = 2V in this circuit?

V1 = 2V represents the initial voltage in the circuit at t=0. It is used as a starting point for calculating the voltage and power at later times.

## What is the role of the inductor in this circuit?

The inductor stores energy in the form of a magnetic field and can cause changes in voltage and current in the circuit.

## How is voltage calculated in this circuit?

Voltage is calculated using Ohm's Law, which states that voltage (V) equals current (I) multiplied by resistance (R). In this circuit, the inductor's resistance (XL) must also be taken into account.

## What is the formula for calculating power in this circuit?

The formula for power in a circuit is P = VI, where P is power in watts, V is voltage in volts, and I is current in amperes. In this circuit, the inductor's resistance and any other resistors must be factored into the calculation.

## At what time (t) does the calculation for voltage and power begin?

The calculation for voltage and power in this circuit begins at t=0, as indicated by the initial voltage value of V1 = 2V. This is the starting point for any subsequent calculations.

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