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enter image description here In the following problem, the equation i(t) = i(∞) + [i(0+) − i(∞)]e^(−t/τ) was used to calculate the current at time t given the initial and final currents. Then, vo(t) was found by equating it to L(di/dt), thee negative of the voltage across the inductor. Instead, why is not possible to use the expression v(t) = v(∞) + [v(0+) − v(∞)]e^(−t/τ) to find v(t) given that v(0) = 6 V and v(∞) = 0 V? Then i(t) could be found by integration, but the results are not consistent. C [![]4

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    \$\begingroup\$ What makes you think it is not possible? Please show us the work that you did. \$\endgroup\$ Apr 19, 2020 at 19:29
  • \$\begingroup\$ Plugging v(0) = 6 V and v(∞) = 0 V into v(t) = v(∞) + [v(0+) − v(∞)]e^(−t/τ), v(t) = [6]e^(−t/τ) which is not consistent with the expression obtained by equating v(t) to Ldi/dt, [4]e^(−t/τ) \$\endgroup\$
    – user402525
    Apr 19, 2020 at 20:12

1 Answer 1

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Your mistake is here: this equation you say is correct:

v(t) = v(∞) + [v(0+) − v(∞)]e^(−t/τ),

but note there is v(0+), not V(0-) = 6 V you are using, and get the wrong result:

v(t) = [6]e^(−t/τ)

The voltage immediately after closing the switch is 4 V, and by placing it to the equation you get the right result:

v(t) = v(∞) + [v(0+) − v(∞)]e^(−t/τ) = 0 V + (4V - 0V)e^(−t/τ)=4Ve^(−t/τ)

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