Respuesta :
Answer:
(a) R = 1Ω
(b) τ = 3
Explanation:
The time constants of the given circuits are as follows
[tex]\tau_{RL} = \frac{L}{R}\\\tau_{RC} = RC[/tex]
If the two circuits have equal time constants, then
[tex]\frac{L}{R} = RC\\R^2 = \frac{L}{C} = \frac{3}{3} = 1\\R = 1\Omega[/tex]
Therefore, the time constant in any of the circuits is
[tex]\tau = RC = 3[/tex]
(a). Value of resistance R is 1 ohm.
(b). The Value of time constant will be 3 second.
The time constant is defined as, time taken by the system to reach at 63.2% of its final value.
Time constant in RL circuit is, [tex]=\frac{L}{R}[/tex]
Time constant in RC circuit is, [tex]=RC[/tex]
Since, in question given that both circuit have same time constant.
So, [tex]RC=\frac{L}{R}\\\\R^{2}=\frac{L}{C}\\\\R=\sqrt{\frac{L}{C} }[/tex]
substituting L = 3H and C = 3F in above expression.
[tex]R=\sqrt{\frac{3}{3} }=1ohm[/tex]
Time constant = [tex]RC=1*3=3s[/tex]
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