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work, resistance and voltage problems

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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?

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?.

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.

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.

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?

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.

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?

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.

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

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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Solution Preview

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

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
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

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

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

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.

See Also This Related BrainMass Solution

Potential difference, Electric field, Equivalent resistance

Please give detailed and clearly explained answers.

1. A uniform electric field E of magnitude 235 N/C is directed in the negative x direction in the Figure 1 in the attachment. The coordinate of point A are (-0.2, -0.3) m, those of point B are (0.4, 0.5) m and those of point C are (-0.2, 0.5) m.

(a) Calculate the potential difference between point A and point C.
(b) Calculate the potential difference between C and B.
(c) Calculate the potential difference between A and B.
(d) Show that the potential difference between A and B is sum of the potential difference between A and C, and the potential difference between C and B.

2. Over a certain region of space, the electric potential is given by :

V(x,y,z) = 5 z - 3 z^2 y + 2 y x^2

(a) Find the expression for the x, y and z components of the electric field over this region.
(b) What is the magnitude of the field at a point P that has coordinates (1, 0, -2)?

3. Refer to the Figure 3 in the attachment, where R1 = 4 Ohm, R2 = 24 Ohm, R3 = 6 Ohm, R4 = 8 Ohm and R5 = 24 Ohm are connected to a battery of 24 V.

(a) Find the equivalent resistance of the circuit.
(b) Find the total current.
(c) Find the current in each resistor (I1, I2, I3, I4 and I5).
(d) Find the voltage across each resistor (V1, V2, V3, V4 and V5).
(e) Find the power delivered to each resistor (P1, P2, P3, P4 and P5).

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