All MCAT Physical Resources
Example Questions
Example Question #33 : Circuits
Consider the following circuit:
Water has been spilt on the circuit, occasionally creating a short in the circuit. The short is represented by the switch, which is closed when the circuit is shorted. What is the difference in power loss through the circuit when the switch is closed compared to being open?
We will need to calculate total equivalent resistance for each of the two scenarios to calculate power losses.
SCENARIO 1: Switch Closed
When the switch is closed, a resistance-free path is created. This effectively reduces the current flow through the parallel resistors to zero. Therefore, we have a much simpler circuit, consisting only of R1 and R5. Since they are in series, we can simply add them:
The expression for power is:
Substituting Ohm's law for current, we get:
Plugging in our values, we get:
SCENARIO 2: Switch Open
Now that we have resistors in parallel, it will take two steps to condense the circuit. For the parallel part, we get:
Now, since everything is in series in this equivalent circuit, we can simply add it all up:
Again using the formula for power, we get:
Now we can calculate the difference between the two scenarios:
Example Question #32 : Circuits
A battery is connected in series with a resistor and a inductor. What is the current in this circuit after a long period of connection?
Relevant equations:
When the circuit is first connected, the current increases from zero to its final value. During this time as the current changes, the inductor has a voltage across it. After a long period, the current has built up to its maximum value.
After a long period, .
Plugging in our values for voltage and resistance, we can solve for the final current.
Example Question #33 : Circuits
An circuit contains a resistor, capacitor, and inductor in series. If this circuit is connected to an AC generator, what angular frequency would maximize the current flow?
Relevant equations:
The current is maximized when the power supply frequency, , equals the resonance frequency, . Plugging in the given inductance and capacitance yields:
Example Question #7 : Current
An circuit consists of a inductor, capacitor, resistor, and a voltage source with maximum voltage of in series. Approximately what is the rms current in this circuit at resonance?
Relevant equations:
at resonance
Step 1: Find impedance, , at resonance:
Step 2: Calculate , using and :
Step 3: Use to calculate :
Example Question #1 : Capacitors And Dielectrics
Capacitors with capacitances of 3 μF, 7 μF and 10 μF are wired in parallel. What is the capacitance of the circuit?
- it cannot be determined without knowing the resistance of the circuit
- it cannot be determined without knowing the time constant in the circuit
- 20 μF
- approximately 1.75 μF
- none of these is correct
3
4
5
2
1
3
Response 3 is the correct choice. Electrons will space themselves as far apart as possible, because of charge repulsion; therefore, in a parallel arrangement, they will jump onto each capacitor and “load it up.” The parallel capacitance is calculated by simply adding the individual values. The value would be about 1.75 μF if the three were connected in series, where the formula is (reciprocal of total equals sum of reciprocal of each). The time constant of a circuit is given by the formula τ = RC, and it relates to how fast a capacitor can charge to full capacitance.
Example Question #41 : Circuits
A and capacitor are connected in series with a 12V battery. What is the maximum charge stored on the capacitor?
First find the equivalent capacitance of the two capacitors by adding their inverses.
Then, we can find the charge stored on this equivalent capacitor.
For capacitors in series the charges on each must be equal, and also equal to the charge on the equivalent capacitor. The answer is .
Example Question #2 : 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.
How is the charge stored on the capacitor?
Evenly distributed inside the capacitor
Evenly distributed on the capacitor surface
Unevenly distributed on the capacitor surface
Unevenly distributed inside the capacitor
Evenly distributed on the capacitor surface
Charge is evenly distributed on the surface of the capacitor. If we think back to electric force, we know that positive charges repel other positive charges and negative charges repel other negative charges; thus, the charges are evenly distributed to minimize the force between them. We can see how this looks in diagrammatic form below.
Example Question #1 : 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.
What is the equivalent capacitance of C2 and C3?
0.33μF
3μF
2μF
0.5μF
0.5μF
First, we need to determine how these capacitors are being added. We can see that they are being added in in series. Remember that capacitors in series are added as reciprocals:
Ceq = 0.5μF
Example Question #1 : 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.
What is the equivalent capacitance of the circuit?
2μF
3μF
4μF
1μF
1μF
First, we need to determine how capacitors C2 and C3 are being added. We can see that they are being added in in series. Remember that capacitors in series are added as reciprocals.
C23 = 0.5μF
Next, we need to determine how we can find the Ceq by simplifying C23 and C1. We can see that Ceq and C1 are in parallel, thus we can directly add the individual capacitances.
Ceq = C23 + C1 = 0.5μF + 0.5μF = 1μF
Example Question #2 : 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.
How long does it take to fully charge the capacitors of the circuit?
1 * 105s
1 * 106s
1 * 103s
1 * 104s
1 * 106s
In order to determine the time, we need to know the total charge stored on the capacitors. Remember that Q = CV, where Q is the total charge, C is the equivalent capacitance, and V is the voltage. 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
Now we can plug in the Ceq and battery voltage to find the charge.
Q = (1μF)(10V) = 10μC
Additionally, we need to know the current the battery can provide (the charge per unit time). Knowing both the total charge and current will allow us to calculate the time. We can use V = IR to determine the current.
I = V/R = 10V/1Ω = 10A = 10C/sec
We can equate charge and current to determine time.
10μC = 10 C/t
t = 10 C/10 μC = 1 * 106s or 11.6days
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