P 7.2-5 The voltage, v(t), and current, i(t), of a 1-F capacitor adhere to the passive convention. Also, v(0) = 0 V and i(0) = 0 A.

(a) Determine v(t) when i(t) = x(t), where x(t) is shown in Figure P 7.2-5 and i(t) has units of A.

(b) Determine i(t) when v(t) = x(t), where x(t) is shown in Figure P 7.2-5 and v(t) has units of V.

Hint: x(t) = 4t – 4 when 1 < t < 2, and x(t) = –4t + 12 when 2 < t < 3.

Figure P 7.2-5

The equation of the curve can be written as :

Current – Voltage relationship for a capacitor can be written either as

or

(a) Determine v(t) when i(t) = x(t), where x(t) is shown in Figure P 7.2-5 and i(t) has units of A.

Use

For

Note

For

Note

For

Note

For

(b) Determine i(t) when v(t) = x(t), where x(t) is shown in Figure P 7.2-5 and v(t) has units of V.

Use

For

For

For

For

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This page last updated on April 3, 2019