Session wise problems - Session 1 Electrical circuits and...

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Session: 1 Electrical circuits and its solution 1. A 30-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1 H and the resistance is 50 ohms. Find the current i t if 0 0 i . Determine the current as t   . 2. A 200-volt electromotive force is applied to an RC-series circuit in which the resistance is 1000 ohms and the capacitance is 6 5 10 farad. Obtain the charge q t on the capacitor if . 4 . 0 0 q . Determine the charge and current at t = 0.005 s. Determine the charge as . t   Home work 1. A 12-volt battery is connected to an LR-series circuit in which the inductance is 0.5 henry and the resistance is 10 ohms. Determine the current i t if the initial current is zero. 2. A 100-volt electromotive force is applied to an RC-series circuit in which the resistance is 200 ohms and the capacitance is 4 10 farad. Determine the charge q(t) on the capacitor if q(0) = 0 also obtain the current i t . Session: 2 Practice problems of electrical circuits through tutorial and MATLAB 1. An electromotive force 120, 0 20 0, 20 t E t t is applied to an LR-series circuit in which the inductance is 20 H and the resistance is 2Ω. Determine the current i t if 0 0. i 2. Determine the current when 2 0.5H, 0.005F, E=2t V, L C and the initial current and charge zero. 3. Determine the current when 0.25H, R 10 , E=48V, L and the initial current and charge zero.
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4. Model the RL -circuit and solve the resulting ODE for the current A (amperes), where t is time. Assume that the circuit contains as an electromotive force a battery of 48 V E t , which is constant, a resistor of 11 R , and an inductor of 0.1H L and that the current is initially zero. Session: 3 Modeling of exponential growth/decay and its solution 1. If the growth rate of a culture of bacteria is proportional to the number of bacteria present and after 1 day is 1.25 times the original number, within what interval of time will the number of bacteria (a) double, (b) triple? 2. The half-life of Carbon -14 is 5730 years. If the decay of Carbon-14 is modeled by the differential equation , du ku dt   where u is the amount of Carbon-14, determine the decay constant. 3. The number N of bacteria in a culture grew at a rate proportional to N. The value of N was initially 125 and increased to 278 in one hour. What would be the value of N after 2 hours? Home work 1. A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. a) Find an expression for the number of bacteria after t hours. b) Find the number of bacteria after 3 hours. c) Find the rate of growth after 3 hours. d) When will the population reach 10,000?
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