### All MCAT Physical Resources

## Example Questions

### Example Question #1 : Current

During the cold winter months, some gloves have the ability to provide extra warmth due to an internal heating source. A simplified circuit, similar to those in electric gloves, is comprised of a 9 V battery with no internal resistance and three resistors as shown in the image below.

What direction do electrons flow through the circuit?

**Possible Answers:**

Clockwise

Counterclockwise

Cannot be determined

**Correct answer:**

Counterclockwise

Remember that convention dictates that current flows in the direction of positive charge (protons), thus, electrons flow in the opposite direction. Also remember that the larger length on the battery symbol on the circuit diagram indicates that current flows in this direction. In the diagram below, we can see that current flows clockwise, thus electrons flow counterclockwise.

### Example Question #2 : Current

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 C_{1} is 0.5 μF and the capacitances of C_{2} and C_{3} are 1 μF each. A 10 V battery with an internal resistance of 1 Ω supplies the circuit.

What direction is current flowing through the circuit?

**Possible Answers:**

Clockwise

Counterclockwise

Cannot be determined

**Correct answer:**

Counterclockwise

Remember that convention dictates that current flows in the direction of positive charge (protons). Also remember that the larger length on the battery symbol on the circuit diagram indicates that current flows in this direction. In the diagram below, we can see that current flows counterclockwise.

### Example Question #3 : Current

During the cold winter months, some gloves have the ability to provide extra warmth due to an internal heating source. A simplified circuit, similar to those in electric gloves, is comprised of a 9V battery with no internal resistance and three resistors as shown in the image below.

How much current flows through resistor R_{4}?

**Possible Answers:**

**Correct answer:**

First, we need to determine the voltage drop across R_{4}. Given that R_{A} and R_{4} are in parallel, we know that the voltage drop across each is the same.

The voltage drop across R_{1} can be calculated using the I_{circuit} (all the current generated by the battery’s potential difference must pass through R_{1} because it is in direct series with the battery), and the resistance of the resistor.

I can be calculated by V = IR because we have the voltage drop across the circuit (9 V) and can calculate the equivalent resistance:

By taking the inverse of the equation, we can see that R_{A4} is equal to 2Ω.

R_{eq} = R_{A4} + R_{1} = 2Ω + 2Ω = 4Ω

Now, using V=IR allows us to find the current in the circuit.

V = IR

I = V/R = 9V/4Ω = 2.25 A

Plugging this value in, we can find the voltage drop across R_{1}.

V_{R1} = IR = (2.25 A)(2Ω) = 4.5 V

Now we can determine the voltage drop across the parallel resistors by subtracting the voltage drop across R_{1} from the battery.

V_{A }= 9V – 4.5V = 4.5V

this value will be the same for either R_{A} or R_{4}. We can now use V = IR to determine the amount of current that flows through R_{4}.

V = IR

I = V/R = 4.5V/3Ω = 1.5A

Additionally, due to Kirchhoff’s first law, we know that current in must equal current out in a junction. Thus, because R_{4} has 1.5 A of current, R_{A} must have 0.75A. Thus makes logical sense because electrons take the path of least resistance, meaning the resistor with the lowest resistance will have the greater current.

### Example Question #4 : Current

During the cold winter months, some gloves have the ability to provide extra warmth due to an internal heating source. A simplified circuit, similar to those in electric gloves, is comprised of a 9V battery with no internal resistance and three resistors as shown in the image below.

What is the current that flows through the circuit?

**Possible Answers:**

**Correct answer:**

Because we are being asked the current that flows through the circuit, we can use the formula V = IR because we have the voltage drop across the circuit (9V) and can calculate the equivalent resistance.

By taking the inverse of the equation, we can see that R_{A4} is equal to 2Ω.

R_{eq} = R_{A4} + R_{1} = 2Ω + 2Ω = 4Ω

Now, using V = IR, we can find the current.

V = IR

I = V/R = 9V/4Ω = 2.25A

### Example Question #5 : Current

If the peak voltage across a resistor in an AC circuit is , what is the rms current across it?

**Possible Answers:**

**Correct answer:**

First, find the rms voltage across the resistor with the equation:

The pure voltage is , allowing us to solve for the rms voltage.

Now we can use Ohm's law to find the rms current.

### Example Question #6 : Current

A 12V battery is connected in a circuit containing two resistors in parallel. The resistors have resistances of and . The resistor is then unscrewed, disconnecting that parallel branch. How does the new current, I_{f}, across the resistor compare to the original current across that resistor, I_{o}?

**Possible Answers:**

**Correct answer:**

Regardless of whether the resistor is present, we can simply focus on the current loop containing the battery and resistor.

For resistors in parallel, each component/branch will have the same voltage drop, but the current may vary. Initially, the voltage through the resistor will be:

After the resistor is removed, the voltage will remain unchanged.

### Example Question #7 : Current

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?

**Possible Answers:**

**Correct answer:**

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 #8 : Current

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?

**Possible Answers:**

**Correct answer:**

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 #9 : Current

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?

**Possible Answers:**

**Correct answer:**

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 #10 : 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?

**Possible Answers:**

**Correct answer:**

Relevant equations:

at resonance

Step 1: Find impedance, , at resonance:

Step 2: Calculate , using and :

Step 3: Use to calculate :

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