Consider the following circuit. We have R_1=7 Ohms, R_2=17 Ohms, R_3=11 Ohms, V=9 Volts, L=0.09 H.
At t=0 the switch is closed.
(a)Immediately after the switch is closed, what are currents I_1, I_2, I_3 ? I_1
(b)What are the three currents after the switch has been closed for a long time?
(c)The switch is now opened again.
(c) What are the three currents after the switch is reopened?
See Related Question: Tue,4-9-13,3:30pm.
I am not getting the answer by solving it. Can u please show the solution again?
Since you did not tell how the 3 resistors and inductor are connected, I
assumed your circuit to be the same
configuration as a selected Related problem. If the assumption is not correct, you cannot get your book's answer. So please explain how your circuit is connected.
To solve this circuit problem, we can use principles from basic circuit analysis and Ohm's law. Let's go step by step to find the solution.
(a) Immediately after the switch is closed, we need to determine the currents I1, I2, and I3.
To find I1, we can use Ohm's law for the resistor R1. Ohm's law states that the current flowing through a resistor is equal to the voltage across the resistor divided by its resistance.
So, using Ohm's law for R1, we have:
I1 = V / R1
Substituting the given values:
I1 = 9 Volts / 7 Ohms
Calculating this, I1 is approximately 1.286 Amperes.
(b) After the switch has been closed for a long time, the circuit will reach a steady-state. In this state, the inductor behaves like a short circuit, and the current will flow along the path of least resistance.
To find the currents after a long time, we can assume that the inductor L is shorted and can be ignored. So, we can disregard its presence in the circuit.
Now, we have a simple series circuit with resistors R1, R2, and R3.
Using Ohm's law for each resistor, we can find the currents.
I1 = V / R1
I2 = V / R2
I3 = V / R3
Substituting the given values:
I1 = 9 Volts / 7 Ohms
I2 = 9 Volts / 17 Ohms
I3 = 9 Volts / 11 Ohms
Calculating these values, the currents I1, I2, and I3 would be approximately:
I1 ≈ 1.286 Amperes
I2 ≈ 0.529 Amperes
I3 ≈ 0.818 Amperes
(c) After the switch is reopened, we need to consider the presence of the inductor in the circuit again. When the switch is open, the inductor will resist changes in the current, and it will try to maintain the same current flow as before the switch was opened.
In this case, after the switch is reopened, the current will try to keep flowing through the inductor, causing a transient effect as the current slowly decreases to zero due to the inductor's inductive properties.
To find the currents after the switch is reopened, we need to analyze the transient behavior of the circuit. This involves solving a differential equation.
However, without knowing the initial conditions and the exact circuit parameters, it is not possible to find the exact solution for the transient currents without further information.
To analyze the transient behavior, one usually needs to solve a differential equation and consider factors like the inductor's inductance, resistance, and the time constant of the circuit.
So, without more information, we cannot accurately determine the exact values of the currents after the switch is reopened.