In the given circuit below inductance values of , and are same. The magnetic energy stored in the entire circuit is

Question

In the given circuit below inductance values of $L_{1}$ , $L_{2}$ and $L_{3}$ are same. The magnetic energy stored in the entire circuit is $(U_{t})$ and that stored in the $L_{2}$ inductor is $(U_{l})$ . $(U_{t} / U_{l})$ is ______. (Ignore the mutual inductance if any) [2026]

Smart Achievers · Accepted Answer

(6)

$Magnetic energy of inductor is U = \frac{1}{2} L i^{2}$

$U_{t} = \frac{1}{2} L I^{2} + \frac{1}{2} L {(\frac{I}{2})}^{2} + \frac{1}{2} L {(\frac{I}{2})}^{2} = \frac{3}{4} L I^{2}$

$U_{ℓ} = \frac{1}{2} L {(\frac{I}{2})}^{2} \Rightarrow \frac{U_{t}}{U_{ℓ}} = 6$

Solution

Q.
In the given circuit below inductance values of $L_{1}$ , $L_{2}$ and $L_{3}$ are same. The magnetic energy stored in the entire circuit is $(U_{t})$ and that stored in the $L_{2}$ inductor is $(U_{l})$ . $(U_{t} / U_{l})$ is ______. (Ignore the mutual inductance if any) [2026]

Ans.
(6)

$Magnetic energy of inductor is U = \frac{1}{2} L i^{2}$

$U_{t} = \frac{1}{2} L I^{2} + \frac{1}{2} L {(\frac{I}{2})}^{2} + \frac{1}{2} L {(\frac{I}{2})}^{2} = \frac{3}{4} L I^{2}$

$U_{ℓ} = \frac{1}{2} L {(\frac{I}{2})}^{2} \Rightarrow \frac{U_{t}}{U_{ℓ}} = 6$

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Solution

Q. In the given circuit below inductance values of L1, L2 and L3 are same. The magnetic energy stored in the entire circuit is (Ut) and that stored in the L2 inductor is (Ul). (Ut/Ul) is ______. (Ignore the mutual inductance if any) [2026]

Ans. (6) Magnetic energy of inductor is U=12Li2 Ut=12LI2+12L(I2)2+12L(I2)2=34LI2 Uℓ=12L(I2)2⇒UtUℓ=6

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Q.
In the given circuit below inductance values of $L_{1}$ , $L_{2}$ and $L_{3}$ are same. The magnetic energy stored in the entire circuit is $(U_{t})$ and that stored in the $L_{2}$ inductor is $(U_{l})$ . $(U_{t} / U_{l})$ is ______. (Ignore the mutual inductance if any) [2026]

Ans.
(6)

$Magnetic energy of inductor is U = \frac{1}{2} L i^{2}$

$U_{t} = \frac{1}{2} L I^{2} + \frac{1}{2} L {(\frac{I}{2})}^{2} + \frac{1}{2} L {(\frac{I}{2})}^{2} = \frac{3}{4} L I^{2}$

$U_{ℓ} = \frac{1}{2} L {(\frac{I}{2})}^{2} \Rightarrow \frac{U_{t}}{U_{ℓ}} = 6$