Explanation of Voltage and Current in a Circuit Element:

Given Data:
- Voltage: v(t) = 100sin(314t + 45)
- Current: i(t) = 10sin(314t + 315)

Understanding the Equations:
- The voltage equation v(t) = 100sin(314t + 45) represents an AC voltage source with an amplitude of 100V and a phase shift of 45 degrees.
- The current equation i(t) = 10sin(314t + 315) represents an AC current flowing through the circuit element with an amplitude of 10A and a phase shift of 315 degrees.

Relationship between Voltage and Current:
- The voltage and current in a circuit element are related by the impedance of the element, which is the ratio of voltage to current.
- In this case, the impedance Z = V/I = 100/10 = 10 ohms.
- The phase relationship between voltage and current is determined by the phase angle difference between the voltage and current waveforms.

Interpretation of the Data:
- The given voltage and current waveforms have the same frequency of 314 Hz.
- The voltage waveform leads the current waveform by 45 degrees, indicating a capacitive circuit element.
- The amplitude of the voltage waveform is higher than the current waveform, reflecting the impedance of the element.

Conclusion:
- By analyzing the given voltage and current waveforms, we can determine the characteristics of the circuit element and understand its behavior in an AC circuit.