Answer :
Final answer:
1. The frequency of the sinusoidal current is approximately 1570 Hertz,
2. the maximum/peak current is 7.5 Amps, the phase angle is approximately 0.61 radians, and 3. the current at t = 97.3µs is calculated by substituting t with 4. 0.0000973 in the equation for I(t).
Explanation:
The expression given I(t) = 7.5 cos(9865t + 35o) is describing an oscillating or sinusoidal current. The information you're looking to find can be determined as follows:
- The frequency (f) in Hertz can be found by using the formula f = ω/2π, where ω (omega) is the angular frequency. In this case, ω = 9865. Thus, f = 9865 / (2π) = approximately 1570 Hz.
- The maximum or peak current (Im) is given by the amplitude of the sinusoid, which in this case is 7.5 Amps.
- The phase angle (Phi) in Radians is derived from the given degree value. In this case, it's 35°, which translates to an equivalent of 35*(π/180) = approximately 0.61 radians.
- The current at time t=97.3 micro-sec can be calculated by substituting t in the equation with 0.0000973, resulting in a value for I(t). I(0.0000973) = 7.5 cos(9865*0.0000973 + 35°).
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