The solution of the following differential equation: \frac{d y}{d x}+\frac{1}{x} y=x y^{2}

The switch in the circuit has been closed for a long time, and it is opened at t=0. Find v(t) for t>= 0. Calculate the initial energy stored in the capacitor. (a). When the switch is closed, calculate the value of Vc. (b). When the switch is opened, find the time constant. (c). Find v(t) for t>= 0. (d). Find p(t) for t>= 0. (e). Calculate the initial energy stored in the capacitor.

2.3 If, for a particular junction, the acceptor concentration is 10 17//cm 3' and the donor concentration is 10 16 cm², a) find the junction built-in voltage. b) Assume n; = 1.5×10 10. Also, find the width of the depletion region (W) and its extent in each of the p and n regions when the junction terminals are left open. c) Calculate the magnitude of the charge stored on either side of the junction. Assume that the junction area is 100 µm².

17 Assuming that the switch in Fig. 7.87 has been in position A for a long time and is moved to position Bat t = 0, Then at t = 1 second, the switch moves from B to C. Find Vc(1) for t>= 0.

Two electric circuits, represented by boxes A and B,are connected as shown in Fig. P1.14. The reference direction for the current i in the interconnection and the reference polarity for the voltage v across the interconnection are as shown in the figure. For each of the following sets of numerical values, calculate the power in the interconnection and state whether the power is flowing from A to B or vice versa. a) i 6 A,v= 30 V b) i -8 A,v = -20 V c) i 4 A,v = -60 V d) i = -9 A,v = 40 V

The manufacturer of a 1.5 V D flashlight battery says that the battery will deliver 9 mA for 40 continuous hours. During that time the voltage will drop from 1.5 V to 1.0 V. Assume the drop in volt-age is linear with time. How much energy does the battery deliver in this 40 h interval?

When a car has a dead battery, it can often be started by connecting the battery from another car across its terminals. The positive terminals are connected together as are the negative terminals. The connection is illustrated in Fig. P1.15. Assume the current iin Fig. P1.15 is measured and found to be 30 A. a) Which car has the dead battery? b) If this connection is maintained for 1 min, how much energy is transferred to the dead battery?

1.4 (a) A particular signal source produces an output of 40 mV when loaded by a 100-k2 resistor and 10 mV when loaded by a 10-k2 resistor. Calculate the Thé venin voltage, Norton current, and source resistance. (b) Using KVL, KCL and Thé venin theorem, compute the Thé venin voltage (Vth) at node A' and Thé venin resistance (Rth) equivalent of the circuit to the left below.

A 1000-MVA, 20-kV, 60-Hz, three-phase generator is connected through a 1000-MVA, 20-kV, Delta-Y transformer to a 345-kV circuit breaker and a 345-kV transmission line. The transformer rated voltage on the high side (Y side) is 345 kV. The generator reactances are X = 0.17 pu, X = 0.30 pu, Xa = 1.5 pu,and its time constants are T 0.05 s,T 1.0 s,TA = 1.10 s. The transformer series reactance is 0.1pu; transformer losses and exciting current are neglected. A three-phase short-circuit occurs on the line side of the circuit breaker when the generator is operated at rated terminal voltage and at no-load. The breaker interrupts the fault three cycles after fault inception. Determine (a) the subtransient current through the breaker in per unit and in kA RMS. (b) The RMS asymmetrical fault current the breaker interrupts,assuming maximum de offset. Neglect the effect of the transformer on the time constants.

Describe the behaviour of the following circuits. In particular explain how the behaviour of the circuits differ from what would be expected if the device was ideal. A voltage is applied to the circuit v(t) as shown. The input voltage is a ramp which starts from 0V at t = 0 and rises to 0.45V over 0.8 sec as shown in the table below. Determine the voltage across the diode and determine if the behaviour is linear. b) For the circuit in figure 3 below explain its function and determine the voltage at the output. (assume the op amp has a +- 12V supply) The input voltage is given in figure 2:-

1.3 The circuit shown below represents the equivalent circuit of an unbalanced bridge. It is required to calculate the current in the detector branch (R5) and the voltage across it. Although this can be done by using loop and node equations, a much easier approach is possible: Find the Thé venin equivalent of the circuit to the left of node 1 and the Thé venin equivalent of the circuit to the right of node 2. Then solve the resulting simplified circuit.