Exam 6: Capacitors and Inductors

The voltage across an inductor with inductance of 510 mH is given by $v ( t ) = \left\{ \begin{array} { c } 0.05 t ^ { 2 } , \quad 0 \leq t < 5 \\0.05 ( t - 10 ) ^ { 2 } , \quad 5 \leq t < 10 \mathrm {~V} \\0 , \quad \text { otherwise }\end{array} \right.$ Find the current through the inductor i(t) and plot the voltage and current as a function of time.

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Question 1

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$i ( t ) = \frac { 1 } { L } \int _ { 0 } ^ { t } v ( \lambda ) d \lambda = \left\{ \begin{array} { c } 0.03268 t ^ { 3 } , \quad 0 \leq t < 5 \\0.03268 t ^ { 3 } - 0.9804 t ^ { 2 } + 9.8039 t - 24.5098 , \quad 5 \leq t < 10 \mathrm {~A} \\8.17 , \quad 10 \leq t\end{array} \right.$
$i ( t ) = \frac { 1 } { L } \int _ { 0 } ^ { t } v ( \lambda ) d \lambda = \left\{ \begin{array} { c } 0.03268 t ^ { 3 } , \quad 0 \leq t < 5 \\ 0.03268 t ^ { 3 } - 0.9804 t ^ { 2 } + 9.8039 t - 24.5098 , \quad 5 \leq t < 10 \mathrm {~A} \\ 8.17 , \quad 10 \leq t \end{array} \right.$
$i ( t ) = \frac { 1 } { L } \int _ { 0 } ^ { t } v ( \lambda ) d \lambda = \left\{ \begin{array} { c } 0.03268 t ^ { 3 } , \quad 0 \leq t < 5 \\ 0.03268 t ^ { 3 } - 0.9804 t ^ { 2 } + 9.8039 t - 24.5098 , \quad 5 \leq t < 10 \mathrm {~A} \\ 8.17 , \quad 10 \leq t \end{array} \right.$

voltage across a capacitor with capacitance of 39 is given by $\mu \mathrm { F }$ $v ( t ) = \left\{ \begin{array} { c } - 30 t , \quad 0 \leq t < 5 \\90 t - 600 , \quad 5 \leq t < 10 \\- 60 t + 900 , \quad 10 \leq t < 15 \\0 , \quad \text { otherwise }\end{array} \right.$ Find the current through the capacitor i(t) and plot the voltage and current as a function of time.

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Question 2

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$i ( t ) = \left\{ \begin{array} { c } - 1.17 , \quad 0 \leq t < 5 \\3.51 , \quad 5 \leq t < 10 \\- 2.34 , \quad 10 \leq t < 15 \\0 , \text { elsewhere }\end{array} \quad \mathrm { mA } \right.$ $i ( t ) = \left\{ \begin{array} { c } - 1.17 , \quad 0 \leq t < 5 \\ 3.51 , \quad 5 \leq t < 10 \\ - 2.34 , \quad 10 \leq t < 15 \\ 0 , \text { elsewhere } \end{array} \quad \mathrm { mA } \right.$

Find the equivalent capacitance between terminals a and b of the circuit shown below.

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Question 3

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$\begin{aligned}\mathrm { L } _ { \mathrm { a } } & = \mathrm { L } _ { 5 } \left\| \mathrm {~L} _ { 6 } \right\| \mathrm { L } _ { 7 } = 27.92 \mathrm { mH } \\\mathrm { L } _ { b } & = \mathrm { L } _ { 3 } + \mathrm { L } _ { \mathrm { a } } = 54.92 \mathrm { mH } \\\mathrm { L } _ { \mathrm { c } } & = \mathrm { L } _ { 2 } \| \mathrm { L } _ { \mathrm { b } } = 21.7457232 \mathrm { mH } \\\mathrm { L } _ { e q } & = \mathrm { L } _ { 1 } + \mathrm { L } _ { \mathrm { c } } = 43.7457232 \mathrm { mH }\end{aligned}$ clear all; format long;
$\mathrm { L } 1 = 22 \mathrm { e } - 3 ; \mathrm { L } 2 = 36 \mathrm { e } - 3 ; \mathrm { L } 3 = 27 \mathrm { e } - 3 ; \mathrm { L } 4 = 75 \mathrm { e } - 3 ; \mathrm { L } 5 = 87 \mathrm { e } - 3 ; \mathrm { L } 6 = 91 \mathrm { e } - 3 ;$
$\mathrm { La } = \mathrm { P } ( [ \mathrm { L } 4 , \mathrm {~L} 5 , \mathrm {~L} 6 ] )$
$\mathrm { Lb } = \mathrm { L } 3 + \mathrm { La }$
$\mathrm { Lc } - \mathrm { P } ( [ \mathrm { L } 2 , \mathrm { Lb } ] )$
$\mathrm { Leq } = \mathrm { L } 1 + \mathrm { Lc }$

find the equivalent capacitance between terminals a and b of the circuit shown below.

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Question 4

current through a capacitor with capacitance of 0.68 is given by i(t) = 4 $\mu \mathrm { F }$ $\sin ( 2 \pi \times 1500 t ) u ( t ) \mathrm { mA }$ . Find the voltage across the capacitor $\mathrm { v } ( \mathrm { t } )$ and plot the current and voltage as a function of time.

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Question 5

Find the equivalent capacitance between terminals a and b of the circuit shown below.

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Question 6

$\text { The current through a capacitor with capacitance of } 33 \mu \mathrm { F } \text { is given by }$ $i ( t ) = \left\{ \begin{array} { c } 0.005 e ^ { - 1000 ( - t + 0.003 ) } , \quad 0 \leq t < 0.003 \\0.005 e ^ { - 1000 ( t - 0.003 ) } , \quad 0.003 \leq t < 0.006 \mathrm {~A} \\0 , \quad \text { otherwise }\end{array} \right.$ $\text { Find the voltage across the capacitor } v ( t ) \text { and plot the current and voltage as a function of time. }$

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Question 7

the voltage across an inductor with inductance of 39 mH is given by $v ( t ) = 6 \cos ( 2 \pi \times 3500 t )$ u(t) V. Find the current through the inductor i(t) and plot the voltage and current as a function of time.

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Question 8

the current through an inductor with inductance of 430 mH is given by $i ( t ) = \left\{ \begin{array} { c } - 4 t , \quad 0 \leq t < 5 \\8 t - 60 , \quad 5 \leq t < 10 \\- 4 t + 60 , \quad 10 \leq t < 15 \\0 , \quad \text { otherwise }\end{array} \mathrm { A } \right.$ Find the voltage across the inductor v(t) and plot the current and voltage as a function of time.

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Question 9

find the equivalent capacitance between terminals a and b of the circuit shown below.

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Question 10

Find the equivalent capacitance between terminals a and b of the circuit shown below.

find the equivalent capacitance between terminals a and b of the circuit shown below.

current through a capacitor with capacitance of 0.68 is given by i(t) = 4 $\mu \mathrm { F }$ $\sin ( 2 \pi \times 1500 t ) u ( t ) \mathrm { mA }$ . Find the voltage across the capacitor $\mathrm { v } ( \mathrm { t } )$ and plot the current and voltage as a function of time.

Find the equivalent capacitance between terminals a and b of the circuit shown below.

the voltage across an inductor with inductance of 39 mH is given by $v ( t ) = 6 \cos ( 2 \pi \times 3500 t )$ u(t) V. Find the current through the inductor i(t) and plot the voltage and current as a function of time.

find the equivalent capacitance between terminals a and b of the circuit shown below.

Voltage, Current, Power, and Sources

Circuit Laws

Circuit Analysis Methods

Circuit Theorems

Operational Amplifier Circuits

RL and RC Circuits

RLC Circuits

Phasors and Impedances

Analysis of Phasor Transformed Circuits

AC Power

Three-Phase Systems

Magnetically Coupled Circuits

The Laplace Transform

Circuits Analysis in the S-Domain

Filters

Exam 6: Capacitors and Inductors

Find the equivalent capacitance between terminals a and b of the circuit shown below.

find the equivalent capacitance between terminals a and b of the circuit shown below.

Find the equivalent capacitance between terminals a and b of the circuit shown below.

the voltage across an inductor with inductance of 39 mH is given by v(t)=6cos⁡(2π×3500t)v ( t ) = 6 \cos ( 2 \pi \times 3500 t )v(t)=6cos(2π×3500t) u(t) V. Find the current through the inductor i(t) and plot the voltage and current as a function of time.

find the equivalent capacitance between terminals a and b of the circuit shown below.

Voltage, Current, Power, and Sources

Circuit Laws

Circuit Analysis Methods

Circuit Theorems

Operational Amplifier Circuits

RL and RC Circuits

RLC Circuits

Phasors and Impedances

Analysis of Phasor Transformed Circuits

AC Power

Three-Phase Systems

Magnetically Coupled Circuits

The Laplace Transform

Circuits Analysis in the S-Domain

Filters

the voltage across an inductor with inductance of 39 mH is given by $v ( t ) = 6 \cos ( 2 \pi \times 3500 t )$ u(t) V. Find the current through the inductor i(t) and plot the voltage and current as a function of time.