(a) The charge q(t) stored on a capacitor having capacitance C (measured in Farads),discharging through a resistor of resistance R (measured in Ohms), is given by q(t)=Q e^{-\frac{t}{R C}} where

Q is the initial charge (measured in Coulombs), andt is time (measured in seconds). Suppose Q = 50 and C= 0.25. (1) For R = 2.5, calculate the charge in the capacitor after 2 seconds have elapsed. Suppose that for a different resistor we are given that 40% of the initial charge isost in the first 3 seconds. Find the value of R.(4 marks) A voltage of the form v = 8 sin(2t) is applied to an electrical circuit. The steady-state output current i flowing through the circuit is given by the sinusoidal oscillation i=2 \sin (2 t)+5 \cos (2 t) The voltage is measured in volts and the current is measured in amps. State the angular frequency of oscillation in radians per second and the fundamental period of oscillation in seconds of the input voltage (that is the minimum time required for a single cycle of oscillation).(2 marks) ) Express the current i in the form i =R sin(wt+a) where a is in radians hence state the amplitude of the output steady state current