Compound Direct Current (DC) Circuits - AP Physics 2
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Determine total voltage in series if $V_1 = 5 \text{V}$ and $V_2 = 3 \text{V}$.
Determine total voltage in series if $V_1 = 5 \text{V}$ and $V_2 = 3 \text{V}$.
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$V_{\text{eq}} = 8 \text{V}$. Series voltages add: $5 + 3 = 8$.
$V_{\text{eq}} = 8 \text{V}$. Series voltages add: $5 + 3 = 8$.
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Calculate total resistance for $R_1 = 3 \text{Ω}$ and $R_2 = 6 \text{Ω}$ in parallel.
Calculate total resistance for $R_1 = 3 \text{Ω}$ and $R_2 = 6 \text{Ω}$ in parallel.
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$R_{\text{eq}} = 2 \text{Ω}$. $\frac{1}{R_{eq}} = \frac{1}{3} + \frac{1}{6} = \frac{1}{2}$.
$R_{\text{eq}} = 2 \text{Ω}$. $\frac{1}{R_{eq}} = \frac{1}{3} + \frac{1}{6} = \frac{1}{2}$.
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What happens to total resistance when a resistor is added in parallel?
What happens to total resistance when a resistor is added in parallel?
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Total resistance decreases. Parallel paths reduce overall resistance.
Total resistance decreases. Parallel paths reduce overall resistance.
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What is the principle of superposition in circuits?
What is the principle of superposition in circuits?
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The voltage/current is the sum of individual contributions. Multiple sources combine linearly in circuit analysis.
The voltage/current is the sum of individual contributions. Multiple sources combine linearly in circuit analysis.
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What is Kirchhoff's Voltage Law?
What is Kirchhoff's Voltage Law?
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The sum of EMFs equals the sum of voltage drops in a loop. Conservation of energy in closed loops.
The sum of EMFs equals the sum of voltage drops in a loop. Conservation of energy in closed loops.
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Calculate power if $I = 5 \text{A}$ and $R = 4 \text{Ω}$.
Calculate power if $I = 5 \text{A}$ and $R = 4 \text{Ω}$.
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$P = 100 \text{W}$. Use $P = I^2R = 5^2 \times 4 = 100$.
$P = 100 \text{W}$. Use $P = I^2R = 5^2 \times 4 = 100$.
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Find power dissipated in a resistor if $I = 4 \text{A}$ and $R = 2 \text{Ω}$.
Find power dissipated in a resistor if $I = 4 \text{A}$ and $R = 2 \text{Ω}$.
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$P = 32 \text{W}$. Use $P = I^2R = 4^2 \times 2 = 32$.
$P = 32 \text{W}$. Use $P = I^2R = 4^2 \times 2 = 32$.
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Calculate total resistance for $R_1 = 4 \text{Ω}$ and $R_2 = 6 \text{Ω}$ in series.
Calculate total resistance for $R_1 = 4 \text{Ω}$ and $R_2 = 6 \text{Ω}$ in series.
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$R_{\text{eq}} = 10 \text{Ω}$. Add series resistances: $4 + 6 = 10$.
$R_{\text{eq}} = 10 \text{Ω}$. Add series resistances: $4 + 6 = 10$.
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What is the formula for equivalent resistance in series?
What is the formula for equivalent resistance in series?
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$R_{\text{eq}} = R_1 + R_2 + \text{...} + R_n$. Resistances add directly in series connections.
$R_{\text{eq}} = R_1 + R_2 + \text{...} + R_n$. Resistances add directly in series connections.
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Calculate current if $Q = 10 \text{C}$ and $t = 5 \text{s}$.
Calculate current if $Q = 10 \text{C}$ and $t = 5 \text{s}$.
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$I = 2 \text{A}$. Apply $I = \frac{Q}{t} = \frac{10}{5} = 2$.
$I = 2 \text{A}$. Apply $I = \frac{Q}{t} = \frac{10}{5} = 2$.
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What is the effect of adding resistors in series on circuit current?
What is the effect of adding resistors in series on circuit current?
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Current decreases. More series resistance increases total resistance.
Current decreases. More series resistance increases total resistance.
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Find power if $V = 10 \text{V}$ and $I = 2 \text{A}$.
Find power if $V = 10 \text{V}$ and $I = 2 \text{A}$.
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$P = 20 \text{W}$. Power equals voltage times current: $10 \times 2$.
$P = 20 \text{W}$. Power equals voltage times current: $10 \times 2$.
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What is the formula for power using voltage and resistance?
What is the formula for power using voltage and resistance?
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$P = \frac{V^2}{R}$. Derived from $P = VI$ and $I = \frac{V}{R}$.
$P = \frac{V^2}{R}$. Derived from $P = VI$ and $I = \frac{V}{R}$.
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What is the relationship between voltage, current, and resistance?
What is the relationship between voltage, current, and resistance?
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Ohm's Law: $V = IR$. Fundamental relationship in electrical circuits.
Ohm's Law: $V = IR$. Fundamental relationship in electrical circuits.
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What is the formula for voltage across a capacitor?
What is the formula for voltage across a capacitor?
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$V = \frac{Q}{C}$. Voltage depends on stored charge and capacitance.
$V = \frac{Q}{C}$. Voltage depends on stored charge and capacitance.
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What is the effect of adding resistors in parallel on circuit current?
What is the effect of adding resistors in parallel on circuit current?
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Current increases. More parallel paths reduce total resistance.
Current increases. More parallel paths reduce total resistance.
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What is Kirchhoff's Current Law?
What is Kirchhoff's Current Law?
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The total current entering a junction equals the total current leaving. Conservation of charge at circuit nodes.
The total current entering a junction equals the total current leaving. Conservation of charge at circuit nodes.
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Find voltage if $I = 3 \text{A}$ and $R = 5 \text{Ω}$.
Find voltage if $I = 3 \text{A}$ and $R = 5 \text{Ω}$.
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$V = 15 \text{V}$. Apply Ohm's law: $V = 3 \times 5 = 15$.
$V = 15 \text{V}$. Apply Ohm's law: $V = 3 \times 5 = 15$.
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What is the formula for power using current and resistance?
What is the formula for power using current and resistance?
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$P = I^2R$. Derived from $P = VI$ and $V = IR$.
$P = I^2R$. Derived from $P = VI$ and $V = IR$.
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Identify the formula for current using charge and time.
Identify the formula for current using charge and time.
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$I = \frac{Q}{t}$. Current is charge flow rate.
$I = \frac{Q}{t}$. Current is charge flow rate.
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Determine total voltage in parallel if $V_1 = 10 \text{V}$ and $V_2 = 10 \text{V}$.
Determine total voltage in parallel if $V_1 = 10 \text{V}$ and $V_2 = 10 \text{V}$.
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$V_{\text{eq}} = 10 \text{V}$. Parallel voltages are equal across branches.
$V_{\text{eq}} = 10 \text{V}$. Parallel voltages are equal across branches.
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Find total current if $V = 12 \text{V}$ and $R = 6 \text{Ω}$.
Find total current if $V = 12 \text{V}$ and $R = 6 \text{Ω}$.
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$I = 2 \text{A}$. Apply $I = \frac{V}{R} = \frac{12}{6} = 2$.
$I = 2 \text{A}$. Apply $I = \frac{V}{R} = \frac{12}{6} = 2$.
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Find energy used in 2 hours if power is $50 \text{W}$.
Find energy used in 2 hours if power is $50 \text{W}$.
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$E = 360,000 \text{J}$. $E = 50 \times 7200 = 360,000$ J.
$E = 360,000 \text{J}$. $E = 50 \times 7200 = 360,000$ J.
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State the formula for electrical energy in terms of power and time.
State the formula for electrical energy in terms of power and time.
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$E = Pt$. Energy equals power multiplied by time.
$E = Pt$. Energy equals power multiplied by time.
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Calculate total energy if $P = 60 \text{W}$ for $3 \text{h}$.
Calculate total energy if $P = 60 \text{W}$ for $3 \text{h}$.
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$E = 648,000 \text{J}$. $E = 60 \times 10800 = 648,000$ J.
$E = 648,000 \text{J}$. $E = 60 \times 10800 = 648,000$ J.
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What happens to total resistance when a resistor is added in series?
What happens to total resistance when a resistor is added in series?
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Total resistance increases. Series resistors add together.
Total resistance increases. Series resistors add together.
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Define electrical power in terms of voltage and current.
Define electrical power in terms of voltage and current.
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$P = VI$. Power is the product of voltage and current.
$P = VI$. Power is the product of voltage and current.
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What is the formula for equivalent resistance in parallel?
What is the formula for equivalent resistance in parallel?
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$\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \text{...} + \frac{1}{R_n}$. Reciprocals add for parallel resistance calculations.
$\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \text{...} + \frac{1}{R_n}$. Reciprocals add for parallel resistance calculations.
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What happens to total resistance when a resistor is added in parallel?
What happens to total resistance when a resistor is added in parallel?
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Total resistance decreases. Parallel paths reduce overall resistance.
Total resistance decreases. Parallel paths reduce overall resistance.
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Calculate total energy if $P = 60 \text{W}$ for $3 \text{h}$.
Calculate total energy if $P = 60 \text{W}$ for $3 \text{h}$.
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$E = 648,000 \text{J}$. $E = 60 \times 10800 = 648,000$ J.
$E = 648,000 \text{J}$. $E = 60 \times 10800 = 648,000$ J.
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