Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centers coinciding. If R1 > > R2, the mutual inductance M between them will be directly proportional to
\(\frac{R_2^2}{R_1}\)
\(\frac{R_1}{R_2}\)
\(\frac{R_2}{R_1}\)
\(\frac{R_1^2}{R_2}\)
The Correct Option is A
Solution and Explanation
Magnetic field at the center of primary coil
\(B=\frac{\mu_0i_1}{2R_1}\)
Now, considering it to be uniform, magnetic flux passing through secondary coil is
\(\phi_2=BA=\frac{\mu_0i_1}{2R_1}(\pi R_{2}^2)\)
Now, \(M=\frac{\phi_2}{i_1}\)
\(=\frac{\mu_0\pi R_{2}^2}{2R_1}\)
\(\therefore\ \ M \propto \frac{R_2^{2}}{R_1}\)
Therefore, the correct option is (A) : \(\frac{R_2^2}{R_1}\).
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Concepts Used:
Inductance
Inductance is a key parameter in electrical and electronic circuit designs. Like resistance and capacitance, it is a basic electrical measurement that affects all circuits to some degree.
Inductance is used in many areas of electrical and electronic systems and circuits. The electronic components can be in a variety of forms and may be called by a variety of names: coils, inductors, chokes, transformers, . . . Each of these may also have a variety of different variants: with and without cores and the core materials may be of different types.
There are two ways in which inductance is used:
- Self-inductance: Self-inductance is the property of a circuit, often a coil, whereby a change in current causes a change in voltage in that circuit due to the magnetic effect of caused by the current flow. It can be seen that self-inductance applies to a single circuit - in other words it is an inductance, typically within a single coil. This effect is used in single coils or chokes.
- Mutual-inductance: Mutual inductance is an inductive effect where a change in current in one circuit causes a change in voltage across a second circuit as a result of a magnetic field that links both circuits. This effect is used in transformers.