MCAT Physical : Electricity and Magnetism
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Example Questions
Example Question #7 : Capacitors And Dielectrics
Batteries and AC current are often used to charge a capacitor. A common example of capacitor use is in computer hard drives, where capacitors are charged in a specific pattern to code information. A simplified circuit with capacitors can be seen below. The capacitance of C1 is 0.5 μF and the capacitances of C2 and C3 are 1 μF each. A 10 V battery with an internal resistance of 1 Ω supplies the circuit.
Instead of air, assume that we insert a dielectric material with a dielectric constant k between the capacitor plates. How would the total capacitance of the circuit change?
Increase
Remain the same
Decrease
Increase
In this question, we are asked how the total charge stored on the surface of the capacitors would change if we inserted a dielectric between the parallel plates. As we can see in the equation for capacitance based on physical properties, 
If we insert a dielectric material, k > 1, the value of C increases, thus the overall capacitance of the circuit increases.
Example Question #1 : Capacitors And Dielectrics
Which of the following statements about dielectrics is false?
A dielectric material increases voltage by decreasing stored charge
A dielectric material increases capacitance by decreasing voltage
A dielectric material is non-conducting
A dielectric material increases capacitance by increasing stored charge
A dielectric material increases voltage by decreasing stored charge
Dielectrics are put between two parallel plates of a capacitor to increase capacitance. This is done by holding voltage constant and increasing charge, or decreasing voltage and holding charge constant.
This can be understood using the equation 
Example Question #9 : Capacitors And Dielectrics
Two capacitors are fully charged and connected in series in a circuit powered by a 
First, we need to find the equivalent capacitance for the capacitors in series.
Now we can find the charge using the equation 
Example Question #41 : Circuits
Two parallel plate capacitors C1 and C2 are arranged in parallel within a 10V circuit. If C1 stores 2C of charge and C2 stores 5C of charge, each over 3 seconds, what is the total capacitance of the circuit?
0.7 F
1.8 F
2.4 F
0.2 F
0.7 F
The capacitance of any capacitor can be calculated with the formula
Since the capacitors are arranged in parallel, the voltage drop across each will be equal, and in this case 10V. Adding capacitors in parallel is the same as adding resistors in series, where the total capacitance of the circuit is equal to the sum of all individual capacitors.
Example Question #81 : Electricity And Magnetism
Batteries and AC current are often used to charge a capacitor. A common example of capacitor use is in computer hard drives, where capacitors are charged in a specific pattern to code information. A simplified circuit with capacitors can be seen below. The capacitance of C1 is 0.5 μF and the capacitances of C2 and C3 are 1 μF each. A 10 V battery with an internal resistance of 1 Ω supplies the circuit.
Capacitors in series share the same __________, while capacitors in parallel share the same __________.
Charge . . . current
Current . . . voltage
Current . . . charge
Voltage . . . current
Current . . . voltage
As with resistors, capacitors in series share the same current. This is a re-statement of the law of conservation of charge. In contrast, capacitors and resistors in parallel share the same voltage.
Example Question #52 : Circuits
Batteries and AC current are often used to charge a capacitor. A common example of capacitor use is in computer hard drives, where capacitors are charged in a specific pattern to code information. A simplified circuit with capacitors can be seen below. The capacitance of C1 is 0.5 μF and the capacitances of C2 and C3 are 1 μF each. A 10 V battery with an internal resistance of 1 Ω supplies the circuit.
How much total charge is stored by the capacitors of the circuit?
25μC
10μC
20μC
15μC
10μC
We are asked how much charge is stored in total on the circuit. We can use the equivalent capacitance and the voltage supplied by the battery to calculate the charge. Remember that Q = CV, where Q is the total charge, C is the equivalent capacitance, and V is the voltage. We must first solve for equivalent capacitance.
C2 and C3 are capacitors in series, while C1 is in parallel.
C23 = 0.5μF
Ceq = C23 + C1 = 0.5μF + 0.5μF = 1μF
Now we can plug in the Ceq and battery voltage to find the charge.
Q = (1μF)(10V) = 10μC
Example Question #53 : Circuits
Batteries and AC current are often used to charge a capacitor. A common example of capacitor use is in computer hard drives, where capacitors are charged in a specific pattern to code information. A simplified circuit with capacitors can be seen below. The capacitance of C1 is 0.5 μF and the capacitances of C2 and C3 are 1 μF each. A 10 V battery with an internal resistance of 1 Ω supplies the circuit.
While the capacitor is charging, does the capacitor generate a magnetic field?
No
Yes
Cannot be determined
Yes
This question asks us to consider electromagnetism and what happens when a capacitor is charging. When a capacitor is charging, charge is accumulating on the surface over a period of time. Given that the electric field due to a capacitor is given by the formula E = σ/ε0, where σ is the charge per unit area and ε0 is the constant of permeability of free space, we can see that E is directly proportional to σ; therefore, the more charge that builds up, the higher the resulting E field.
Because σ is changing during charging, and thus E is changing, we also know that a magnetic field, B, must be created.
Remember the principle—a changing electric field induces a changing magnetic field, and a changing magnetic field induces a changing electric field.
Example Question #54 : Circuits
Batteries and AC current are often used to charge a capacitor. A common example of capacitor use is in computer hard drives, where capacitors are charged in a specific pattern to code information. A simplified circuit with capacitors can be seen below. The capacitance of C1 is 
How much potential energy is stored by the capacitors of the circuit?
First, we need to determine the type of energy being stored by the capacitors in the circuit. As this is an electric circuit, electric energy is being stored. Thus, we can use the formula for potential energy stored in a capacitor, U = ½CV2. We must first find the equivalent capacitance.
C2 and C3 are capacitors in series, while C1 is in parallel.
C23 = 0.5μF
Ceq = C23 + C1 = 0.5μF + 0.5μF = 1μF
U = ½CV2 = ½(1μF)(10V)2 = 5 * 10-5J
Example Question #55 : Circuits
Which of the following arrangements of parallel conducting plates would store the most charge when connected in series with a battery of voltage 
Assume that in each arrangement, each plate has area 
Plates separated of 
Plate separation of 
Plate separation of 
Plate separation of 
Plate separation of 
Plate separation of
Relevant equations:
The first equation shows that charge 
The second equation shows that 
A smaller distance 
Example Question #56 : Circuits
An RC circuit is assembled by connecting a voltage source, a resistor, and a capacitor in series. The capacitor in the circuit has a potential difference of 
To solve this question, we need to use the equation that describes voltage decay during capacitor discharging:
Here, 
To remove the exponential 
Solving for 
The time constant, 
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