Final answer:
To find the instantaneous current i(t) for a non-sinusoidal voltage applied to a resistor-capacitor load, calculate capacitive reactance for each frequency, use Ohm's law to determine current from voltage and impedance, and sum the phasor components.
Step-by-step explanation:
To determine the instantaneous current i(t) through the load consisting of a 10 ohm resistor in series with a 0.5 mF capacitor, we must solve the given non-sinusoidal voltage source, v(t) = 40\u221A2 cos(200t) + 60\u221A2 sin(100t).
The first step is to calculate the impedance of the capacitor at the given frequencies. The formula for the capacitive reactance is XC = 1 / (\u03C9C), where \u03C9 is the angular frequency and C is the capacitance in farads.
Once the capacitive reactance at each frequency is determined, we can use the impedance to find the current components due to each part of the voltage source using Ohm's law, I = V / Z, where Z is the impedance and can be calculated as Z = \u221A(R2 + XC2) for each frequency. Then, by using the phasor addition, we can find the total current i(t).