bedblogi38am
2022-05-18
Answered

How much power is produced if a voltage of 4V is applied to a circuit with a resistance of $27\mathrm{\Omega}$ ?

You can still ask an expert for help

Lucille Lucas

Answered 2022-05-19
Author has **16** answers

Probably not a lot more explanation needed. We are given a voltage (V) And a resistance ($\mathrm{\Omega}$). We know that the expression for power in a circuit is P=VI, but we don't know the current.

We do know a way to find the current, given the voltage and the resistance: Ohm's Law :

V=IR

Rearranging:

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

We could calculate the current and then substitute that into the expression for the power, but I decided to combine the equations instead:

$P=VI=V(\frac{V}{R})=\frac{{V}^{2}}{R}$

Then it's just a matter of substituting in the values we have and we know the power produced by the circuit.

We do know a way to find the current, given the voltage and the resistance: Ohm's Law :

V=IR

Rearranging:

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

We could calculate the current and then substitute that into the expression for the power, but I decided to combine the equations instead:

$P=VI=V(\frac{V}{R})=\frac{{V}^{2}}{R}$

Then it's just a matter of substituting in the values we have and we know the power produced by the circuit.

asked 2022-05-08

How can we evaluate

${\int}_{0}^{1}\frac{{\mathrm{log}}^{2}(x+1)\mathrm{log}({x}^{2}+1)}{{x}^{2}+1}dx$

Any kind of help is appreciated.

${\int}_{0}^{1}\frac{{\mathrm{log}}^{2}(x+1)\mathrm{log}({x}^{2}+1)}{{x}^{2}+1}dx$

Any kind of help is appreciated.

asked 2022-04-06

A submarine of mass m is travelling at max power and has engines that deliver a force F at max power to the submarine. The water exerts a resistance force proportional to the square of the submarine's speed v.

The submarine increases its speed from ${v}_{1}$ to ${v}_{2}$, show that the distance travelled in this period is $\frac{m}{2k}\mathrm{ln}\frac{F-k{v}_{1}^{2}}{F-k{v}_{2}^{2}}$ where k is a constant.

I've found $\frac{dv}{dt}=\frac{1}{m}(F-k{v}^{2})$ using $\sum F=ma$ but I am struggling to progress further using integration or the fact that $\frac{dv}{dt}=v\frac{dv}{dx}=\frac{d}{dx}(\frac{1}{2}{v}^{2})=\frac{{d}^{2}x}{d{t}^{2}}$ which is how I've been taught to solve resisted motion questions.

The submarine increases its speed from ${v}_{1}$ to ${v}_{2}$, show that the distance travelled in this period is $\frac{m}{2k}\mathrm{ln}\frac{F-k{v}_{1}^{2}}{F-k{v}_{2}^{2}}$ where k is a constant.

I've found $\frac{dv}{dt}=\frac{1}{m}(F-k{v}^{2})$ using $\sum F=ma$ but I am struggling to progress further using integration or the fact that $\frac{dv}{dt}=v\frac{dv}{dx}=\frac{d}{dx}(\frac{1}{2}{v}^{2})=\frac{{d}^{2}x}{d{t}^{2}}$ which is how I've been taught to solve resisted motion questions.

asked 2022-05-18

If $a,b,c\in (0,\mathrm{\infty})$ with abc=1 prove:

${a}^{2}+{b}^{2}+{c}^{2}+3(ab+bc+ca)\le \frac{1}{2}(\sqrt{a}+\sqrt{b}+\sqrt{c})(a+b)(b+c)(c+a).$

On atypical inequality (a smaller amount than a product) that resisted my attempts to prove it.

${a}^{2}+{b}^{2}+{c}^{2}+3(ab+bc+ca)\le \frac{1}{2}(\sqrt{a}+\sqrt{b}+\sqrt{c})(a+b)(b+c)(c+a).$

On atypical inequality (a smaller amount than a product) that resisted my attempts to prove it.

asked 2022-05-14

How to prove ${\int}_{0}^{1}\frac{1+{x}^{30}}{1+{x}^{60}}dx=1+\frac{c}{31}$, where 0

asked 2022-05-19

What is the electric current produced when a voltage of 24V is applied to a circuit with a resistance of $8\mathrm{\Omega}$?

asked 2021-03-01

Answer the following T/F questions based on the behavior of the circuit in the above Figure 5:

(1) A transient current flows for a short time after the RELAY is switched to either the N.O.("normally open") or N.C. ("normally closed") position.

(2)The transient currents that flow in this experiment decays exponentially to zero.

(3)The capacitor charge Q exponentially decays to zero when the RELAY is thrown to position N.O.

(4)When the current I is positive, the capacitor charge Q is decreasing.

(5)When the current I is positive, the measured VOLTAGE IN 2 will be negative.

(6)When the capacitor charge Q is positive, the measured VOLTAGE IN 1 is positive.

(7)The quantity t1/2=? ln 2 is called the half-life of an exponential decay, where ?=RC is the time constant in an RC circuit. The current in a discharging RC circuit drops by half whenever t increases by $t}_{\frac{1}{2}$. For a circuit with R=2 k? and C=3 ?F, if the current is 6 am at t=5 ms, at what time (in ms) will the current be 3 mA?

asked 2021-11-21

An oil pump is drawing 44 kW of electric power while pumping oil with ρ= 860 kg/m^3 at a rate of 0.1 m^3/s. The inlet and outlet diameters of the piper are 8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is measured to be 500 kPa and the motor efficiency is 90 percent, determine the mechanical efficiency of the pump.