Circuits with Resistors and Inductors - AP Physics C: Electricity and Magnetism
Card 1 of 30
Determine the total power $P$ dissipated in an LR circuit.
Determine the total power $P$ dissipated in an LR circuit.
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$P = I^2R$. Only resistor dissipates power as heat.
$P = I^2R$. Only resistor dissipates power as heat.
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If $\theta = 45^\circ$, what is the relationship between $R$ and $X_L$?
If $\theta = 45^\circ$, what is the relationship between $R$ and $X_L$?
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$R = X_L$. At 45°, resistive and reactive parts are equal.
$R = X_L$. At 45°, resistive and reactive parts are equal.
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State the formula for the time constant $\tau$ in an LR circuit.
State the formula for the time constant $\tau$ in an LR circuit.
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$\tau = \frac{L}{R}$. Time constant determines how quickly current changes.
$\tau = \frac{L}{R}$. Time constant determines how quickly current changes.
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Which component causes a phase shift between voltage and current in an LR circuit?
Which component causes a phase shift between voltage and current in an LR circuit?
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Inductor. Inductors oppose current changes, creating phase lag.
Inductor. Inductors oppose current changes, creating phase lag.
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Calculate $I(t)$ at $t=2\tau$ during discharging if $I_0 = 10,A$.
Calculate $I(t)$ at $t=2\tau$ during discharging if $I_0 = 10,A$.
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$I(t) = 1.35,A$. $I = 10 \times e^{-2} = 1.35,A$
$I(t) = 1.35,A$. $I = 10 \times e^{-2} = 1.35,A$
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Calculate energy stored in an inductor with $L=4,H$ and $I=2,A$.
Calculate energy stored in an inductor with $L=4,H$ and $I=2,A$.
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$16,J$. $U = \frac{1}{2} \times 4 \times 2^2 = 16,J$
$16,J$. $U = \frac{1}{2} \times 4 \times 2^2 = 16,J$
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What is the current $I(t)$ at $t=\tau$ in an LR circuit during charging?
What is the current $I(t)$ at $t=\tau$ in an LR circuit during charging?
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$I(t) = 0.632I_0$. At one time constant, $1-e^{-1} = 0.632$
$I(t) = 0.632I_0$. At one time constant, $1-e^{-1} = 0.632$
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What is the effect of $L$ on the phase angle $\theta$ if $L$ increases?
What is the effect of $L$ on the phase angle $\theta$ if $L$ increases?
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Increases. Higher $L$ increases $X_L$, increasing phase angle.
Increases. Higher $L$ increases $X_L$, increasing phase angle.
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Find $Z$ if $R=6,\Omega$ and $X_L=8,\Omega$ in an LR circuit.
Find $Z$ if $R=6,\Omega$ and $X_L=8,\Omega$ in an LR circuit.
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$Z = 10,\Omega$. $Z = \sqrt{6^2 + 8^2} = 10,\Omega$
$Z = 10,\Omega$. $Z = \sqrt{6^2 + 8^2} = 10,\Omega$
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Determine $X_L$ if frequency $f$ is doubled in an LR circuit.
Determine $X_L$ if frequency $f$ is doubled in an LR circuit.
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Doubles. Reactance linearly proportional to frequency.
Doubles. Reactance linearly proportional to frequency.
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Find $Z$ if $R=6,\Omega$ and $X_L=8,\Omega$ in an LR circuit.
Find $Z$ if $R=6,\Omega$ and $X_L=8,\Omega$ in an LR circuit.
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$Z = 10,\Omega$. $Z = \sqrt{6^2 + 8^2} = 10,\Omega$
$Z = 10,\Omega$. $Z = \sqrt{6^2 + 8^2} = 10,\Omega$
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What is the phase angle $\theta$ in an LR circuit?
What is the phase angle $\theta$ in an LR circuit?
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$\theta = \tan^{-1}(\frac{X_L}{R})$. Phase angle shows current lagging behind voltage.
$\theta = \tan^{-1}(\frac{X_L}{R})$. Phase angle shows current lagging behind voltage.
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What is the time-dependent current $I(t)$ in an LR circuit during discharging?
What is the time-dependent current $I(t)$ in an LR circuit during discharging?
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$I(t) = I_0 e^{-\frac{t}{\tau}}$. Exponential decay from initial current.
$I(t) = I_0 e^{-\frac{t}{\tau}}$. Exponential decay from initial current.
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What is the energy stored in an inductor $L$ with current $I$?
What is the energy stored in an inductor $L$ with current $I$?
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$\frac{1}{2}LI^2$. Magnetic field energy in inductor.
$\frac{1}{2}LI^2$. Magnetic field energy in inductor.
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Calculate $I(t)$ at $t=2\tau$ during discharging if $I_0 = 10,A$.
Calculate $I(t)$ at $t=2\tau$ during discharging if $I_0 = 10,A$.
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$I(t) = 1.35,A$. $I = 10 \times e^{-2} = 1.35,A$
$I(t) = 1.35,A$. $I = 10 \times e^{-2} = 1.35,A$
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Calculate the power factor $pf$ in an LR circuit.
Calculate the power factor $pf$ in an LR circuit.
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$pf = \cos(\theta)$. Cosine of phase angle between voltage and current.
$pf = \cos(\theta)$. Cosine of phase angle between voltage and current.
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Identify the formula to calculate the impedance $Z$ in an LR circuit.
Identify the formula to calculate the impedance $Z$ in an LR circuit.
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$Z = \sqrt{R^2 + (X_L)^2}$. Impedance combines resistance and inductive reactance.
$Z = \sqrt{R^2 + (X_L)^2}$. Impedance combines resistance and inductive reactance.
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What is the time-dependent current $I(t)$ in an LR circuit during discharging?
What is the time-dependent current $I(t)$ in an LR circuit during discharging?
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$I(t) = I_0 e^{-\frac{t}{\tau}}$. Exponential decay from initial current.
$I(t) = I_0 e^{-\frac{t}{\tau}}$. Exponential decay from initial current.
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What happens to impedance $Z$ if resistance $R$ decreases in an LR circuit?
What happens to impedance $Z$ if resistance $R$ decreases in an LR circuit?
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Decreases. Lower resistance reduces total impedance.
Decreases. Lower resistance reduces total impedance.
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In an LR circuit, what happens to current $I(t)$ as time $t \rightarrow \infty$ during charging?
In an LR circuit, what happens to current $I(t)$ as time $t \rightarrow \infty$ during charging?
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Approaches $I_0$. Current reaches steady-state value over time.
Approaches $I_0$. Current reaches steady-state value over time.
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Calculate energy stored in an inductor with $L=4,H$ and $I=2,A$.
Calculate energy stored in an inductor with $L=4,H$ and $I=2,A$.
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$16,J$. $U = \frac{1}{2} \times 4 \times 2^2 = 16,J$
$16,J$. $U = \frac{1}{2} \times 4 \times 2^2 = 16,J$
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What is the time-dependent current $I(t)$ in an LR circuit during charging?
What is the time-dependent current $I(t)$ in an LR circuit during charging?
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$I(t) = I_0(1 - e^{-\frac{t}{\tau}})$. Exponential rise to steady-state current.
$I(t) = I_0(1 - e^{-\frac{t}{\tau}})$. Exponential rise to steady-state current.
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Determine the total power $P$ dissipated in an LR circuit.
Determine the total power $P$ dissipated in an LR circuit.
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$P = I^2R$. Only resistor dissipates power as heat.
$P = I^2R$. Only resistor dissipates power as heat.
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What is the energy stored in an inductor $L$ with current $I$?
What is the energy stored in an inductor $L$ with current $I$?
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$\frac{1}{2}LI^2$. Magnetic field energy in inductor.
$\frac{1}{2}LI^2$. Magnetic field energy in inductor.
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If resistance $R$ doubles in an LR circuit, what happens to the time constant $\tau$?
If resistance $R$ doubles in an LR circuit, what happens to the time constant $\tau$?
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Halved. Time constant inversely proportional to resistance.
Halved. Time constant inversely proportional to resistance.
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Predict the phase difference between current and voltage in an LR circuit.
Predict the phase difference between current and voltage in an LR circuit.
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Current lags voltage. Inductor causes current to lag voltage.
Current lags voltage. Inductor causes current to lag voltage.
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Calculate the time constant $\tau$ for $L=3,H$ and $R=6,\Omega$ in an LR circuit.
Calculate the time constant $\tau$ for $L=3,H$ and $R=6,\Omega$ in an LR circuit.
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$\tau = 0.5,s$. $\tau = \frac{3}{6} = 0.5,s$
$\tau = 0.5,s$. $\tau = \frac{3}{6} = 0.5,s$
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Find the inductive reactance $X_L$ if $L=2,H$ and $f=50,Hz$.
Find the inductive reactance $X_L$ if $L=2,H$ and $f=50,Hz$.
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$X_L = 628.32,\Omega$. $X_L = 2\pi \times 50 \times 2 = 628.32,\Omega$
$X_L = 628.32,\Omega$. $X_L = 2\pi \times 50 \times 2 = 628.32,\Omega$
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Determine the impedance $Z$ if $R=3,\Omega$ and $X_L=4,\Omega$.
Determine the impedance $Z$ if $R=3,\Omega$ and $X_L=4,\Omega$.
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$Z = 5,\Omega$. $Z = \sqrt{3^2 + 4^2} = 5,\Omega$
$Z = 5,\Omega$. $Z = \sqrt{3^2 + 4^2} = 5,\Omega$
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Find the phase angle $\theta$ if $R=5,\Omega$ and $X_L=12,\Omega$.
Find the phase angle $\theta$ if $R=5,\Omega$ and $X_L=12,\Omega$.
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$\theta = 67.38^\circ$. $\theta = \tan^{-1}(\frac{12}{5}) = 67.38°$
$\theta = 67.38^\circ$. $\theta = \tan^{-1}(\frac{12}{5}) = 67.38°$
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