As per the given figure, if $\frac{ dI }{ dt }=-1 A /$ s then the value of $V _{ AB }$ at this instant will be ______$V$
As per the given figure, if $\frac{ dI }{ dt }=-1 A /$ s then the value of $V _{ AB }$ at this instant will be ______$V$
Correct Answer: 30
Solution and Explanation
The correct answer is 30.
Applying Kirchhoff's Voltage Law (KVL):
The differential equation for the circuit is given by:
\[ \frac{dI}{dt} = -1 \ \text{A/sec} \]
The equation for the potential difference across the circuit is:
\[ V_A - IR - L \frac{dI}{dt} - 12 = V_B \]
Substituting Known Values:
Substitute \(I = 2 \ \text{A}\), \(R = 12 \ \Omega\), \(L = 6 \ \text{H}\), and \(\frac{dI}{dt} = -1\):
\[ V_A - 2 \times 12 - 6(-1) - 12 = V_B \]
Simplify the equation:
\[ V_A - V_B = 36 - 6 = 30 \ \text{volts} \]
Final Answer:
\(V_A - V_B = 30 \ \text{volts}\)
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.