Q1. (a) A coil of resistance R ohms and inductance L henrys is connected in series with a capacitor of C farads across ac supply of v volts. Determine EACH of the following for the circuit:
(i) The impedance Z ohms, in complex cartesian form, given that
Z = R + j (ωL - 1/ωC)
where R = 4 ohms, ω = 100 π, L = 0.04 henrys and C = 150 × 10- 6 farads. (4)
(ii) The current, i amps, in polar forms given that i = v/Z and v = 100 volts. (6)
(b) The characteristic impedance, Z, of a transmission line is given by Z = √((R + j ωL)/(G + j ω C))
Determine the condition, in terms of R, L, G and C, that the impedance will be real. (6)
Q2. (a) Solve the following system of equations for x and y.(10)
x2 + 5xy - 4y2 = - 10
2x + 5y = 1
(b) The formula M = (wx (l - x))/2 gives the bending moment M at a point in a beam.
Calculate the values of x, correct to 3 decimal places, when M = 65, l = 25 and w = 2.5. (6)
Q3. (a) A propulsion problem causes a reduction in a ship’s speed of 3.5 knots throughout a passage of 630 nautical miles, resulting in the ship arriving at its destination 6 hours behind schedule. Calculate the passage time. (10)
(b) The minimum diameter, d, of a shaft subjected to a bending moment M and torque T is given by the formula
d3 = 16/(π f) [M + √(M2 + T2 )]
Transpose the formula to obtain T. (6)
Username or email address *Required
Password *Required
Note: Entering wrong username in the login form will ban your IP address immediately. Entering wrong password multiple times will also ban your IP address temporarily.
Log in
Lost your password? Remember me
No account yet?
