Two inductors of self-inductances L 1 and L 2 and of resistances R 1 and R 2 (not shown here) respectively, are connected in the circuit as shown in Fig. At the instant t = 0, key K is closed. Obtain an expression for which the galvanometer will show zero deflection at all times after the key is closed.
Text Solution
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Sol. Since there is no current through BD therefore points B and D are at the same Potential
v B = v D
Potential difference, V AB = V AD
L 1 
+ i 1 R 1 = L 2 
+ i 2 R 2 .…. (1)
Similarly, V BC = V DC
i 1 R 3 = i 2 R 4 ….. (2)
From equations (1) and (2),
R 3 = 
R 4
or 
= 
i 1 = i 2 
L 1 
+ i 2 
= L 2 
+ i 2 R 2
= i 2 
….. (3)
At t = 0, i 2 = 0
∴ L 1 
– L 2 = 0 as 
≠ ≠ 0
∴ 
= 
….. (4)
At t = ∞ , 
= 0 i 2 = 
= constant
⇒ R 2 – 
= 0
∴ 
= 
….. (5)
From eqns. (4) and (5), 
= 
= 
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