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work, resistance and voltage problems

(See attached file for full problem description and diagrams)

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3.
The filament of a light bulb has a resistance of 580 Ω. A voltage of 120 V is connected across the filament. How much current is in the filament?

13.
A cylindrical copper cable carries a current of 1200 A. There is a potential difference of 1.6 X 10-2 V between two points of the cable that are 0.24 m apart. What is the radius of the cable?.

25.
A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 11 A, and that of the vacuum cleaner is 4.0 A. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 15 minutes to the energy used by the vacuum cleaner in one-half hour.

35.
An electric furnace runs nine hours a day to heat a house during January (31 days). The heating element has a resistance of 5.3 Ω and carries a current of 25 A. The cost of electricity is $0.10/kWh. Find the cost of running the furnace for the month of January.

41.
A 36.0-Ω resistor and an 18.0-Ω resistor are connected in series across a 15.0-V battery. What is the voltage across (a) the 36.0-Ω resistor and (b) the 18.0-Ω resistor?

67.
A new "D" battery has an emf of 1.5 V. When a wire of negligible resistance is connected between the terminals of the battery, a current of 28 A is produced. Find the internal resistance of the battery.

75.
Two batteries, each with an internal resistance of 0.015 Ω, are connected as in the drawing. In effect, the 9.0-V battery is being used to charge the 8.0-V battery. What is the current in the circuit?

83.
A galvanometer with a coil resistance of 12.0 Ω and a full-scale current of 0.15 mA is used with a shunt resistor to make an ammeter. The ammeter registers a maximum current of 4.00 mA. Find the equivalent resistance of the ammeter.

87.
Determine the equivalent capacitance between A and B for the group of capacitors in the drawing.

95.
The circuit in the drawing contains two resistors and two capacitors that are connected to a battery via a switch. When the switch is closed, the capacitors begin to charge up. What is the time constant for the charging process?

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(See attached file for full problem description and diagrams)

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3.)
Resistance R = 580 ohm
potential difference V = 120 V
Therefore, current
I = V/R = 120/580 = 0.207 == 0.21 A --Answer

13.)
current I = 1200 A
potential difference, V = 1.6*10^(-2) V
length, L = 0.24 m
resistivity or specific resistance of copper, rho = 1.682 * 10^(-8) ohm.m

Because, resistance R = V/I = 1.6*10^(-2)/1200 = 1.33*10^(-5) ohm
Because,
R = rho*L/A
=> area of cross-section A = rho*L/R = 1.682 * 10^(-8)*0.24/1.33*10^(-5) = 3.0276*10^(-4) m^2
A = pi*r^2
=> radius, r = sqrt(A/pi) = sqrt(3.0276*10^(-4)/3.14) = 9.9*10^(-3) m --Answer

25.)
voltage V = 120 V
current in dryer, Id = 11.0 A
current in vacuum tube, Iv = 4.0 A

a.) Power consumed by dryer,
Pd = V*Id = 120*11.0 = 1320.00 W --Answer

b.)
Power consumed by vacuum cleaner,
Pv = V*Iv = 120*4.0 = 480.00 w --Answer

c.)
Energy by dryer in 15 min/energy by Vacuum cleaner in half hr = ...

Solution Summary

Work over circuits are discussed. Electricity, capacitance, voltage, resistance are explored in a variety of different questions.

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