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Consider a lead acid battery with 100 Ah capacity and a rated voltage of $12 \mathrm{~V}$. (a) What is the total capacity of energy in watt-hours that can be stored in the battery? (b) Assume that the battery is at $40 \%$ of its rated capacity. The battery is now charging at a C-rate of 2 C. What is the charging current that is going into the battery? (c) How much time will it take for the battery to increase the SoC from $40 \%$ to $100 \%$, assuming a constant C-rate of $2 \mathrm{C}$ ? You may assume a linear rate of charging. (d) If the voltaic efficiency of the battery is $90 \%$, and the coulombic efficiency of the battery is $90 \%$, how high is the round-trip efficiency of storage?

Consider a lead acid battery with 100 Ah capacity and a rated voltage of $12 \mathrm{~V}$. (a) What is the total capacity of energy in watt-hours that can be stored in the battery? (b) Assume that the battery is at $40 \%$ of its rated capacity. The battery is now charging at a C-rate of 2 C. What is the charging current that is going into the battery? (c) How much time will it take for the battery to increase the SoC from $40 \%$ to $100 \%$, assuming a constant C-rate of $2 \mathrm{C}$ ? You may assume a linear rate of charging. (d) If the voltaic efficiency of the battery is $90 \%$, and the coulombic efficiency of the battery is $90 \%$, how high is the round-trip efficiency of storage?

Solar Energy: The Physics and Engineering of Photovoltaic Conversion, Technologies and Systems

Use the function to find (a) the image of $v$ and (b) the preimage of $\mathbf{w}$. $$\begin{aligned}&T\left(v_{1}, v_{2}\right)=\left(\frac{\sqrt{2}}{2} v_{1}-\frac{\sqrt{2}}{2} v_{2}, v_{1}+v_{2}, 2 v_{1}-v_{2}\right),\\&\mathbf{v}=(1,1), \mathbf{w}=(-5 \sqrt{2},-2,-16)\end{aligned}$$

Use the function to find (a) the image of $v$ and (b) the preimage of $\mathbf{w}$. $$\begin{aligned}&T\left(v_{1}, v_{2}\right)=\left(\frac{\sqrt{2}}{2} v_{1}-\frac{\sqrt{2}}{2} v_{2}, v_{1}+v_{2}, 2 v_{1}-v_{2}\right),\\&\mathbf{v}=(1,1), \mathbf{w}=(-5 \sqrt{2},-2,-16)\end{aligned}$$

Elementary Linear Algebra

Linear Transformations

Introduction to Linear Transformations

An electron that has an instantaneous velocity of $$ \vec{v}=\left(2.0 \times 10^{6} \mathrm{m} / \mathrm{s}\right) \hat{\mathrm{i}}+\left(3.0 \times 10^{6} \mathrm{m} / \mathrm{s}\right) \hat{\mathrm{j}} $$ is moving through the uniform magnetic field $\vec{B}=(0.030 \mathrm{T}) \hat{\mathrm{i}}-$ $(0.15 \mathrm{T}) \hat{\mathrm{j}} .(\mathrm{a})$ Find the force on the electron due to the magnetic field. (b) Repeat your calculation for a proton having the same velocity.

An electron that has an instantaneous velocity of $$ \vec{v}=\left(2.0 \times 10^{6} \mathrm{m} / \mathrm{s}\right) \hat{\mathrm{i}}+\left(3.0 \times 10^{6} \mathrm{m} / \mathrm{s}\right) \hat{\mathrm{j}} $$ is moving through the uniform magnetic field $\vec{B}=(0.030 \mathrm{T}) \hat{\mathrm{i}}-$ $(0.15 \mathrm{T}) \hat{\mathrm{j}} .(\mathrm{a})$ Find the force on the electron due to the magnetic field. (b) Repeat your calculation for a proton having the same velocity.

Fundamentals of Physics

Questions asked

ANSWERED

Vishal Gupta verified

Numerade educator

B I I R I

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ANSWERED

Aparna Shakti verified

Numerade educator

V1 = 15V R1 = 20? I1 L1 R2 = 10? R3 = 8? R4 = 5? I2 V2 = 12V I3 L2 R5 = 3? V3 = 8V

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