Determine v(t) for t2 0 for the circuit of Figure P 7.2-10a when v(0) = -4 V and is(t) is the current shown in Figure. Find the value of A,B,C,D and E. The value of v(t) for the time interval 0 ≤ t≤ 0.25 is in the form A+Bt² The value of v(t) for the time interval 0.25 ≤t≤ 0.5 is in the form C+Dt The value of v(t) for the time interval 0.5 ≤ t is in the form E is (t) M 2Ω + 0.1 F= v(t) -

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I cant solve for part C and I don't know what I am doing wrong and still ending up with the overall right answer. 

This graph depicts the current \( i_S \) in amperes (A) as a function of time \( t \) in seconds (s). The vertical axis represents the current, with markings at 1 and 2 amperes, while the horizontal axis represents time, marked at 0.25 and 0.5 seconds.

**Graph Description:**
- The graph begins at the origin (0,0), indicating a zero current at time \( t = 0 \).
- From \( t = 0 \) to \( t = 0.25 \) seconds, the current linearly increases, reaching a maximum of 2 amperes.
- Between \( t = 0.25 \) and \( t = 0.5 \) seconds, the current remains constant at 2 amperes.
- After \( t = 0.5 \) seconds, the current abruptly returns to zero amperes.

This graph is labeled "(b)" below the horizontal axis. It visually represents a piecewise linear function, showing the rising, constant, and falling phases of the current over the specified time interval.
Transcribed Image Text:This graph depicts the current \( i_S \) in amperes (A) as a function of time \( t \) in seconds (s). The vertical axis represents the current, with markings at 1 and 2 amperes, while the horizontal axis represents time, marked at 0.25 and 0.5 seconds. **Graph Description:** - The graph begins at the origin (0,0), indicating a zero current at time \( t = 0 \). - From \( t = 0 \) to \( t = 0.25 \) seconds, the current linearly increases, reaching a maximum of 2 amperes. - Between \( t = 0.25 \) and \( t = 0.5 \) seconds, the current remains constant at 2 amperes. - After \( t = 0.5 \) seconds, the current abruptly returns to zero amperes. This graph is labeled "(b)" below the horizontal axis. It visually represents a piecewise linear function, showing the rising, constant, and falling phases of the current over the specified time interval.
**P7.2.10 (Questions 1 to 5)**

Determine \( v(t) \) for \( t \geq 0 \) for the circuit of Figure P 7.2-10a when \( v(0) = -4 \, \text{V} \) and \( i_s(t) \) is the current shown in Figure. **Find the value of A, B, C, D, and E.**

The value of \( v(t) \) for the time interval \( 0 \leq t \leq 0.25 \) is in the form 

\[ A + Bt^2 \]

The value of \( v(t) \) for the time interval \( 0.25 \leq t \leq 0.5 \) is in the form 

\[ C + Dt \]

The value of \( v(t) \) for the time interval \( 0.5 \leq t \) is in the form 

\[ E \]

**Diagram Description:**

The circuit diagram (Figure P 7.2-10a) consists of a simple series circuit with the following components:
- A current source \( i_s(t) \) oriented upwards.
- A resistor with a resistance of \( 2 \, \Omega \) connected in series with the current source.
- A capacitor with a capacitance of \( 0.1 \, \text{F} \) connected across the output, with its voltage designated as \( v(t) \). 

The positive terminal of the capacitor is on the top, indicating the direction of positive voltage.
Transcribed Image Text:**P7.2.10 (Questions 1 to 5)** Determine \( v(t) \) for \( t \geq 0 \) for the circuit of Figure P 7.2-10a when \( v(0) = -4 \, \text{V} \) and \( i_s(t) \) is the current shown in Figure. **Find the value of A, B, C, D, and E.** The value of \( v(t) \) for the time interval \( 0 \leq t \leq 0.25 \) is in the form \[ A + Bt^2 \] The value of \( v(t) \) for the time interval \( 0.25 \leq t \leq 0.5 \) is in the form \[ C + Dt \] The value of \( v(t) \) for the time interval \( 0.5 \leq t \) is in the form \[ E \] **Diagram Description:** The circuit diagram (Figure P 7.2-10a) consists of a simple series circuit with the following components: - A current source \( i_s(t) \) oriented upwards. - A resistor with a resistance of \( 2 \, \Omega \) connected in series with the current source. - A capacitor with a capacitance of \( 0.1 \, \text{F} \) connected across the output, with its voltage designated as \( v(t) \). The positive terminal of the capacitor is on the top, indicating the direction of positive voltage.
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