Solved: In the circuit in Fig. P 7 . 1 2 , the voltage and current expressions are 𝑣 = 4 0 0 𝑒 – 5 𝑡 𝑉 , 𝑡 ≥ 0 + 𝑖 = 1 0 𝑒 – 5 𝑡 𝐴 , 𝑡 ≥ 0

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7.12 In the circuit in Fig. P7.12, the voltage and current expressions are

𝑣=400𝑒-5𝑡𝑉,𝑡≥0+

𝑖=10𝑒-5𝑡𝐴,𝑡≥0

Find

a) 𝑅.

b) 𝜏 (in milliseconds).

c) 𝐿.

d) the initial energy stored in the inductor.

e) the time (in milliseconds) it takes to dissipate 80% of the initial stored energy.

Figure P7.12

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Solved: In the circuit in Fig. P 7 . 1 2 , ﻿the voltage and current expressions are 𝑣 = 4 0 0 𝑒 – 5 𝑡 𝑉 , 𝑡 ≥ 0 + 𝑖 = 1 0 𝑒 – 5 𝑡 𝐴 , 𝑡 ≥ 0

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Solved: In the circuit in Fig. P 7 . 1 2 , the voltage and current expressions are 𝑣 = 4 0 0 𝑒 – 5 𝑡 𝑉 , 𝑡 ≥ 0 + 𝑖 = 1 0 𝑒 – 5 𝑡 𝐴 , 𝑡 ≥ 0