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AP Physics 1 : Electricity and Waves

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Example Questions

Example Question #2 : Understanding Circuit Diagrams

Circuit diagram

V=5V

$R_1=1\Omega$

$R_2=4\Omega$

In the circuit above, what is the total current?

Possible Answers:

20A

6.25A

Correct answer:

6.25A

Explanation:

To find the amperage, first find the combined resistances of the resistors in parallel:

$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}=\frac{1}{1\Omega }+\frac{1}{4\Omega }$

$\frac{1}{R_T}=\frac{5}{4\Omega }$

$R_T=\frac{4}{5}\Omega$

After that, calculate the current using Ohm's Law:

$I=\frac{V}{R}=\frac{5V}{\frac{4}{5}\Omega}$

I=6.25A

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Example Question #2 : Understanding Circuit Diagrams

Circuit diagram

I=30A

$R_1=2\Omega$

$R_2=3\Omega$

In the circuit above, what is the total voltage?

Possible Answers:

30V

25V

75V

36V

150 V

Correct answer:

36V

Explanation:

To find the voltage, first find the combined resistances of the resistors in parallel:

$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}=\frac{1}{2\Omega }+\frac{1}{3\Omega }$

$\frac{1}{R_T}=\frac{5}{6\Omega }$

$R_T=\frac{6}{5}\Omega$

Use Ohm's law to find the voltage.

V=IR

$V=30A\left(\frac{6}{5}\Omega\right)=36V$

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Example Question #3 : Understanding Circuit Diagrams

Circuit diagram

V=5V

I=1.25A

$R_1=6\Omega$

In the circuit above, what is the resistance of R_2 ?

Possible Answers:

$2\Omega$

$-2\Omega$

$12\Omega$

$2.4\Omega$

$10\Omega$

Correct answer:

$12\Omega$

Explanation:

Find the total resistance of the circuit, which can be determined using Ohm's law.

V=IR

$R_T=\frac{V}{I}$

$R_T=\frac{5}{1.25}\Omega=4\Omega$

Now, the resistance of the second resistor can be found. Since the two resistors are in parallel, they're related to the total resistance as follows:

$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}$

Rearrange and solve for R_2

$\frac{1}{R_2}=\frac{1}{R_T}-\frac{1}{R_1}$

$\frac{1}{R_2}=\frac{1}{4\Omega }-\frac{1}{6\Omega }=\frac{6-4}{24\Omega }=\frac{1}{12\Omega }$

$R_2=12\Omega$

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Example Question #5 : Understanding Circuit Diagrams

Circuit diagram2

$R_1=3\Omega$

$R_2=6\Omega$

$R_3=2\Omega$

$R_4=16\Omega$

In the circuit above, what is the total resistance?

Possible Answers:

$\frac{9}{32}\Omega$

$\frac{34}{5}\Omega$

$27\Omega$

$\frac{27}{2}\Omega$

$\frac{34}{9}\Omega$

Correct answer:

$\frac{34}{9}\Omega$

Explanation:

Find the combined resistances for the resistors in parallel:

$\frac{1}{R_A}=\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{1}{R_A}=\frac{1}{3\Omega}+\frac{1}{6\Omega}=\frac{9}{18\Omega}$

$R_A=2\Omega$

$\frac{1}{R_B}=\frac{1}{R_3}+\frac{1}{R_4}$

$\frac{1}{R_B}=\frac{1}{2\Omega}+\frac{1}{16\Omega}=\frac{18}{32\Omega}$

$R_B=\frac{16}{9}\Omega$

Combine these two combined series resistors to find the total resistance:

$R_T=R_A+R_B=2\Omega+\frac{16}{9}\Omega=\frac{34}{9}\Omega$

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Example Question #4 : Understanding Circuit Diagrams

Circuit diagram2

$R_1=1\Omega$

$R_2=2\Omega$

$R_3=3\Omega$

$R_4=4\Omega$

V=10V

In the circuit above, what is the voltage drop across R_3 ?

Possible Answers:

12.6 V

5.4V

1.3V

2.8 V

7.2V

Correct answer:

7.2V

Explanation:

Find the total resistance of the circuit. First, calculate the values of the combined resistances of the resistors in parallel:

$\frac{1}{R_A}=\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{1}{R_A}=\frac{1}{1\Omega}+\frac{1}{2\Omega}=\frac{3}{2\Omega}$

$R_A=\frac{2}{3}\Omega$

$\frac{1}{R_B}=\frac{1}{R_3}+\frac{1}{R_4}$

$\frac{1}{R_B}=\frac{1}{3\Omega}+\frac{1}{4\Omega}=\frac{7}{12\Omega}$

$R_B=\frac{12}{7}\Omega$

Therefore, the total resistance is:

$R_T=R_A+R_B=\frac{2}{3}\Omega+\frac{12}{7}\Omega=\frac{50}{21}\Omega$

Now, note that since R_3 and R_4 are in parallel, the voltage drop across them is the same. Use Ohm's law to relate current in terms of voltage and resistance.

$I=\frac{V_T}{R_T}$

Substitute into Ohm's law for the resistance across R_3 :

$V_{3,4}=\frac{V}{R_T}R_B$

$V_{3,4}=10V\left(\frac{21}{50\Omega}\right)\left(\frac{12\Omega}{7}\right)$

$V_{3,4}=7.2V$

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Example Question #1311 : Ap Physics 1

Circuit diagram2

$R_1=1\Omega$

$R_2=2\Omega$

$R_3=3\Omega$

$R_4=4\Omega$

V=10V

In the circuit above, what is the current passing through R_3 ?

Possible Answers:

4.2A

1.4A

2.4A

1.8A

2.8A

Correct answer:

2.4A

Explanation:

Find the total resistance of the circuit. First, calculate the values of the combined resistances of the resistors in parallel:

$\frac{1}{R_A}=\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{1}{R_A}=\frac{1}{1\Omega}+\frac{1}{2\Omega}=\frac{3}{2\Omega}$

$R_A=\frac{2}{3}\Omega$

$\frac{1}{R_B}=\frac{1}{R_3}+\frac{1}{R_4}$

$\frac{1}{R_B}=\frac{1}{3\Omega}+\frac{1}{4\Omega}=\frac{7}{12\Omega}$

$R_B=\frac{12}{7}\Omega$

Therefore, the total resistance is:

$R_T=R_A+R_B=\frac{2}{3}\Omega+\frac{12}{7}\Omega=\frac{50}{21}\Omega$

From Ohm's law, we know that $\frac{V}{R_T}$ is the current traveling through the circuit.

$I=10V\left(\frac{21}{50\Omega}\right)=4.2A$

This current will be divided between and , with more current taking the path of lower resistance.

Total voltage drop across $R_{3,4}$ :

$V_{3,4}=I_TR_{3,4}$

$V_{3,4}=4.2A\cdot\frac{12}{7}\Omega$

$V_{3,4}=7.2V$

V_3=V_4=7.2V

The current through R_3 is given by:

$I_3=\frac{V_3}{R_3}$

$I_3=\frac{7.2V}{3\Omega}=2.4A$

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Example Question #11 : Understanding Circuit Diagrams

Circuitdiagram3

$R_1=3\Omega$

$R_2=6\Omega$

$R_3=2\Omega$

$R_4=10\Omega$

In the circuit above, what is the total resistance?

Possible Answers:

$21\Omega$

$\frac{80}{21}\Omega$

$\frac{21}{80}\Omega$

$\frac{21}{108}\Omega$

$\frac{108}{21}\Omega$

Correct answer:

$\frac{80}{21}\Omega$

Explanation:

Begin by combining the resistors that are immediately in series:

$R_A=R_1+R_3=3\Omega+2\Omega=5\Omega$

$R_B=R_2+R_4=6\Omega+10\Omega=16\Omega$

Circuit diagramab

Now to find the total resistance, combine these two new resistance values, which are in parallel:

$\frac{1}{R_T}=\frac{1}{5\Omega}+\frac{1}{16\Omega}=\frac{21}{80\Omega}$

$R_T=\frac{80}{21}\Omega$

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Example Question #11 : Understanding Circuit Diagrams

Circuitdiagram3

$R_1=1\Omega$

$R_2=2\Omega$

$R_3=3\Omega$

$R_4=4\Omega$

V=10V

In the circuit above, what is the voltage drop across R_3 ?

Possible Answers:

3.3V

2.5 V

5.0V

6.7V

7.5V

Correct answer:

7.5V

Explanation:

To approach this problem, note that there are no other resistors (or combinations or resistors) beyond the parallel arrangement shown, so the voltage drop across the top (R_1,R_3) and the bottom (R_2,R_4) is the same and equal to the voltage across the circuit, 10V .

The voltage drop across R_3 can be found as:

$V_3=\frac{R_3}{R_1+R_3}V=\frac{3\Omega}{1\Omega+3\Omega}10V=\frac{3}{4}\cdot10V$

V_3=7.5V

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Example Question #12 : Understanding Circuit Diagrams

Circuitdiagram3

$R_1=1\Omega$

$R_2=2\Omega$

$R_3=3\Omega$

$R_4=4\Omega$

V=10V

In the circuit above, what is the current passing through R_3 ?

Possible Answers:

0.625A

1.667A

2.5A

1.875A

4.167A

Correct answer:

2.5A

Explanation:

To approach this problem, note that there are no other resistors (or combinations or resistors) beyond the parallel arrangement shown, so the voltage drop across the top (R_1,R_3) and the bottom (R_2, R_4) is the same and equal to the voltage across the circuit, 10V .

Furthermore, the current that passes through R_1 must be the same as the current that passes through R_3 .

Therefore, the current that passes through them can be found by rearranging Ohm's law, solving for current.

$I_{1,3}=\frac{V}{R_1+R_3}=\frac{10V}{1\Omega+3\Omega}$

$I_{1,3}=2.5A$

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Example Question #13 : Understanding Circuit Diagrams

Basic circuit2

In the circuit above:

$V_{in}=12V$

$Z_1=11\Omega$

$Z_2=21\Omega$

$Z_3=16\Omega$

What is the current across Z_3 ?

Possible Answers:

0.38A

2.25A

1.13A

1.50A

0.75A

Correct answer:

0.75A

Explanation:

The quickest way to approach this problem is to realize that the voltage drop across Z_3 is the same as the voltage drop across the combined resistances of Z_1 and Z_2 . Since this parallel combination is the only presence of resistance in the circuit, this voltage drop must be the total voltage of the circuit, 12V .

Therefore, the current across Z_3 is:

$I_3=\frac{V_3}{Z_3}$

$I_3=\frac{12V}{16\Omega}$

I_3=0.75A

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AP Physics 1 : Electricity and Waves

Study concepts, example questions & explanations for AP Physics 1

All AP Physics 1 Resources

Example Questions

Example Question #2 : Understanding Circuit Diagrams

Example Question #2 : Understanding Circuit Diagrams

Example Question #3 : Understanding Circuit Diagrams

Example Question #5 : Understanding Circuit Diagrams

Example Question #4 : Understanding Circuit Diagrams

Example Question #1311 : Ap Physics 1

Example Question #11 : Understanding Circuit Diagrams

Example Question #11 : Understanding Circuit Diagrams

Example Question #12 : Understanding Circuit Diagrams

Example Question #13 : Understanding Circuit Diagrams

All AP Physics 1 Resources

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