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An aluminium wire with a square cross-section 4 mm on a side is carrying a current of 4.5 amps. Aluminium has a resistivity of 2.69 × 10−6 ohm-cm and an atomic volume of 10 cc/mol. Assuming aluminium has three free electrons per atom, calculate the (a) Hall coefficient, (b) electric field, (c) power dissipated (heat generated) per cm length, and (d) the Hall voltage across the wire in a transverse magnetic field of 1 tesla.
A solenoid of length 2.2 m has a diameter of 0.9 m. The magnetic field at its centre is 0.4 tesla. Estimate the energy stored in the field of this coil.
By considering the principles that the distribution of current in a circuit is the result of charge conservation, and the distribution of potential differences in a circuit is the result of energy conservation, derive:
(a) the combined resistance of two resistors R1 and R2 connected in series (4 marks)
(b) the combined resistance of two resistors R1 and R2 connected in parallel.
The efficiency of a small electric motor is being investigated. It is set up to lift a mass while the current and potential difference are both monitored. The measurements are as follows:
Mass raised = 500 g Height raised = 1.2 m
Time taken = 12 s Potential difference = 3.2 V Current = 0.6 A.
(a) Calculate the work done on the mass
(b) Calculate the useful power output of the motor
(c) Calculate the electrical power supplied
(d) Calculate the efficiency of the motor
(e) What happened to the energy that was ‘lost’?
Find the equivalent capacitance.
C1=6.0 µF, C=4.0 µF
Find the equivalent capacitance.
C1=2.0 µF, C2=2.5 µF, C3=4.5 µF, C4=7.5 µF, C5=5.0 µF
Find the equivalent capacitance.
C1=5.0 µF, C2=3.5 µF, C3=8.0 µF, C4=1.5 µF, C5=0.75µF, C6=15 µF
A simple circuit is constructed in which a 1 Ω resistor is connected across a 1 V battery and so draws a 1 A current. What is the current drawn from the battery if:
(a) an extra 1 Ω resistor is connected in series with the existing one?
(b) four extra 1 Ω resistors are connected in series with the existing one?
Five resistors are connected to a 24 V resistor as shown.
(a) What is the total resistance of the circuit?
(b) How much current flows from the battery?
(c) How much power is supplied by the battery?
(d) What is the potential difference across each resistor?
(e) What is the current through each resistor?
(f) What is the power dissipated in each resistor?
ZL = 200 Ω and it is desired that Zi = 50 Ω The quarter wave transformer should have a characteristic impedance of
A. 100 Ω
B. 40 Ω
C. 10000 Ω
D. 4 Ω
