Physical Setting / Physics Regents Examinations: Solved Electricity Problems Using Equations

Electricity
Note: Each solved problem is preceded by a formula.


EL1.



EXAMPLE: Two small charged spheres are 3.0 meters apart, and each sphere has a charge of 2.0 × 10-6 coulomb. Calculate the magnitude of the force exerted by one sphere on the other.





EL2.



EXAMPLE: When a charge of 0.040 coulomb is placed at a point in the electric field, the force on the charge is 100 newtons. What is the magnitude of the electric field at that point?





EL3.



EXAMPLE: The work required to move a charge of 0.04 coulomb from one point to another in an electric field is 200 joules.





EL4.



EXAMPLE: Calculate the current in a conductor if 130 coulombs of charge is transferred in 20.0 seconds.





EL5.



EXAMPLE: A resistor has a resistance of 10 ohms and a current in it of 0.50 ampere. What is the potential difference across the resistor?





EL6.



EXAMPLE: Calculate the resistance of a bar of silver if its length is 2.00 meters and its cross-sectional area is 0.0100 meter2.

Use Reference Table J to obtain the resistivity of silver (1.59 × 10–8 Ω·m).





EL7.




a. P = VI

EXAMPLE: The potential difference across a resistor is 15 volts and the current in it is 0.50 ampere.




b. P = I2R

EXAMPLE: The current in a resistor is 3.0 ampere, and its resistance is 10 ohms.




c.



EXAMPLE: The potential difference across a resistor is 100 volts, and its resistance is 50.0 ohms.





EL8.




a. W = Pt

EXAMPLE: An electric toaster rated at 1500 watts is used for 40 seconds. How much energy does it use?




b. W = VIt

EXAMPLE: The potential difference across a resistor is 15 volts and the current in it is 0.50 ampere. How much energy is used by the resistor in 5.0 minutes when operating at the rated power?




c. W = I2Rt

EXAMPLE: The current in a resistor is 3.0 ampere, and its resistance is 10. ohms. How much energy is used by the resistor in 5.0 minutes?





EL9A. Series Circuit: I = I1 = I2 = I3 = …

EXAMPLE: In a series circuit containing three resistors having resistances of 5, 10, and 15 ohms, respectively, we know that the current in the 15-ohm resistor is 0.5 ampere. This tells us that the current is also 0.5 ampere in the 5-ohm and 10-ohm resistors as well as in the generator connected to the circuit.



EL9B. Series Circuit: V = V1 + V2 + V3 + …

EXAMPLE: In the circuit described in the previous question, if we know that the voltages across the three resistors are 2.5, 5.0, and 7.5 volts, respectively, then the voltage supplied by the source is the sum of these three values, namely 15 volts.



EL9C. Series Circuit: Req = R1 + R2 + R3 + …

EXAMPLE: In the circuit described in the previous two questions, we can add the individual resistances to get the total resistance.





EL10A. Parallel Circuit: I = I1 + I2 + I3 + …

EXAMPLE: A parallel circuit has two branches, a 10-ohm resistor connected parallel to a 20-ohm resistor. If the current in the 10-ohm resistor is 6.0 amperes, and the current in the 20-ohm resistor is 3.0 amperes, how much current is supplied by the source?





EL10B. Parallel Circuit: V = V1 = V2 = V3 = …

In a parallel circuit the potential difference of the source is equal to the potential difference across each of the branches.


EXAMPLE: If the potential difference across the 20-ohm resistor is 60 volts, what is the potential difference supplied by the source?





EL10C. Parallel Circuit:



In a parallel circuit the reciprocal of the total resistance (or equivalent resistance) is equal to the sum of the reciprocals of the individual resistances.


EXAMPLE: In the circuit described in the previous two questions, what is the total resistance of the circuit?