Passive Elements in the Series Circuit:

In the given series circuit, there are two passive elements present. To determine these elements, let's analyze the given current and applied voltage expressions.

1. Voltage Expression:
The applied voltage expression is given as V = 200sin(2000t + 50), where:
- Amplitude: 200
- Angular frequency: 2000 rad/s
- Phase angle: 50 degrees

From this expression, we can conclude that the applied voltage is an alternating voltage with a sinusoidal waveform. The amplitude represents the maximum value of the voltage, and the angular frequency determines the rate of change of the sinusoidal waveform.

2. Current Expression:
The current expression is given as I = 4cos(2000t + 13.2), where:
- Amplitude: 4
- Angular frequency: 2000 rad/s
- Phase angle: 13.2 degrees

Similar to the voltage expression, the current expression represents an alternating current with a cosine waveform. The amplitude represents the maximum value of the current, and the angular frequency determines the rate of change of the cosine waveform.

Comparison and Analysis:
To determine the elements present in the circuit, we need to analyze the relationship between the voltage and current expressions. In a series circuit, the current flowing through each element is the same. Therefore, we can compare the voltage and current expressions to identify the elements.

Comparing the voltage and current expressions, we can observe the following:

1. The voltage expression is a sine function, while the current expression is a cosine function. This indicates that there is a phase difference between the voltage and current.

2. The phase angle of the voltage expression is 50 degrees, while the phase angle of the current expression is 13.2 degrees. The phase difference between the voltage and current is given by the difference in their phase angles.

Conclusion:
Based on the analysis, we can conclude that the series circuit contains the following passive elements:

1. Resistor: The presence of a phase difference between the voltage and current indicates the presence of a resistor. A resistor is a passive element that dissipates energy and converts it into heat.

2. Inductor: The phase difference between the voltage and current also suggests the presence of an inductor. An inductor is a passive element that stores energy in the form of a magnetic field.

Therefore, the series circuit contains both a resistor and an inductor as passive elements.