impedance-is-the-resistance-to-the-flow-of-current-in-an-electric-circuit-measured-in-ohms-the-imped

Question

Impedance is the resistance to the flow of current in an electric circuit measured in ohms.
The impedance, $Z,$ in a circuit is found by using the formula $Z=\frac{V}{I}$ where $V$ is the voltage
(measured in volts) and $I$ is the current (measured in amperes). Find the impedance when
$V=1.8-0.4 i$ volts and $I=-0.3 i$ amperes.

Heather Zimmers · Accepted Answer

All right. So here we have an application of complex numbers. We have the electric circuit. Z is impedance these voltage eyes current, and we were given some numbers for voltage and current and were asked to find the impedance. So let&#x27;s go ahead and substitute those into the equation. And we have 1.8 minus 0.4 i over negative 0.3 I. Now let&#x27;s go ahead and change that to standard form so we should multiply the numerator and denominator by I that&#x27;ll do it. Weaken, weaken multiplied by more later if we need to. So that ends up giving us 1.8 I minus 0.4. I squared over negative 0.3 times I squared and everywhere we see I squared, we can replace it with negative one. So we have 1.8 I minus 0.4 times negative, one over negative, 0.3 times negative one. Let&#x27;s simplify that a little bit more and we have 1.8 I plus 0.4 divided by 0.3. And to finish this off writing it in standard form, the rial part would be 0.4 divided by 0.3 and that simplifies to be 4/3. And then the imaginary part is going to be 1.8. I divided by 0.31 point eight divided by 80.3 is six. So that&#x27;s going to be six I. So we get 4/3 plus six I

Julie Silva · Answer

So in this problem, we were given this formula. Z is equal divvy, divided by I or via cell voltage. And I represents the number of em peers in order to find Z, which is the impending It&#x27;s well, they tell us that the voltage is 18 plus I, as I noted here, and they tell us that there&#x27;s three minus four I and Piers. So I said, I t equal three minus four I Well, if we&#x27;re looking for the impending, it&#x27;s we&#x27;re looking for Z So all we need to do is substitute are expressions for V and I into our formula. So that&#x27;s going to give us an V Z equals 18. Plus I divided by to remind us for I and then we just need to simplify. Remember, we can&#x27;t have a complex number in the denominator of our fraction. So we need to multiply the numerator and denominator by the conjugated of three minus four I, which is three plus four I. So to multiply our new Marie, there&#x27;s we can use the foil method Well, 18 times three is 54 and 18 times four. I is equal to 72 I I times three is positive. Three I and I times four I is equal to positive for I square now for a denominator were just multiplying con tickets. So all we need to dio is multiply the real parts three times three, which is nine. And then multiply the imaginary parts. Negative four I times four I which is negative. 16 I square. All right, let&#x27;s go back to simplifying or numerator. Well, I&#x27;m gonna bring down our first term which is 54 then we have, like, terms 72 y plus three I, which is 75 I and then our last term has I square than it which remember is equal to negative one. Well, four times negative one is negative for now in denominator Gonna bring down the nine. We also have a nice squared in our last term. Well, negative 16 times Negative one is positive. 16. Well, I see we have, like, terms still in the numerator we have 54 minus four with just 50. So we have 50 plus 75 I divided by nine plus 16 which is 25. So the last thing we need to dio is divide both terms in the numerator by our denominator. Well, 50 divided by 25 is too. And 75 I divided by 25 is three I. And so now we&#x27;ve found the amount of impending. And if you wanted to put in a units with this, remember, it&#x27;s in terms of homes. So our answer would be to plus three i homes.

Ankit Gupta · Answer

we have to find impure insect we have given that wall days is equal toe in Plus, I owe tabbouleh and current element. I is equal to three minus four iota amperes. Now that is a quart of walt age over I, which is equal toe 18 plus iota over three minus four iota. Now rationalize this. We get it in. Plus, I would stop by three minus four iota into tree plus four iota by three plus four iota. Now my deploying this Tom&#x27;s we get 18 plus iota three plus four iota divided by three whole square minus four iota Whole square which implies that 54 last 72 hours plus three iota plus four I&#x27;ll square whole divided by nine minus 16 Iron square. No, simplify this. We get 54 plus 75 iota minus four because I oughta square is equal to minus one. Divided by nine plus 16 which is equal to 50 plus 75 iota by 25 which implies that 50 by 25 plus 75 by 25. I owe talk which is acquired two plus three I s O that is equal to two plus three iota sold. The impudence is equal to two plus three iota home, which is a very quiet answer

Julie Silva · Answer

So in this problem, they give us the formula. V equals Isay, where V represents the voltage. I represents the current and Ze represents the independence. Well, they tell us that the current which is I, is represented by the complex number 0.5 plus 2.0 I. And they tell us that the impending Vince is represented by the complex number 0.4 minus 3.0. I we want to find the voltage. Well, to do this, we simply need to substitute are complex number for I infer I in the equation and we&#x27;re going to substitute the complex number for Z in frizzy. So what we&#x27;re going to have is V equals the quantity of 0.5 plus 2.0 i times to quantity of 0.4 minus 3.0 I. And so now all we need to do is multiply these values together. So we&#x27;re going to do this using the foil method. So we&#x27;re gonna have V equals well, 0.5 times 0.4 is 0.2. Next for multiply 0.5 times 3.0, which is 1.5. Excuse me. Negative 1.5 I. Next we&#x27;re going to multiply 2.0 times 0.4, which is positive. 0.8 I. And lastly, we need to multiply 2.0 i by negative 3.0 I, which is negative. Six. I squared, and now we just need to simplify. Well, we&#x27;re gonna bring down that first term of 0.2 because it has nothing to combine with now. Our next two terms are like terms. Well, negative. 1.5 I plus 0.8 I is negative 0.7 I. Now, For our last term, we have a nice square which remember, is negative one. So we can rewrite this as negative six times negative one. Well, negative. Six times negative One is positive. Six. So we have 0.2 minus 0.7 I plus six. And now we can combine 0.2 plus six, which is 6.2. So our final answer the voltage will be 6.2 minus 0.7

Christina Shute · Answer

in this problem we&#x27;re solving for the value of V or volts. Now, the equation we&#x27;re going to use to solve Urbi is the equals I multiplied by C. So the first thing we&#x27;re gonna do is substitute our values into this equation. So we have B equals three minus two. I multiplied by five plus five. I note that I did not include the own symbol which is a unit of measurement, not a mathematical symbol. So looking at this multiplication, we&#x27;re going to use the foil method to guide our work. So we have first fifteens outside. We have plus 15 eyes inside minus 10 eyes last minus 10. I squared, combine like terms and we get 15 plus five I minus 10. I squared, you recalled that I squared equals negative one sort of a substitute that into our equation to continue simplifying. So we get 15 plus five I plus 10 combine like terms t finish out our solution. We get 20. Sorry, but 25 plus five I and that&#x27;s involved since standard form. So we

Jeremy Strong · Answer

are in this problem were given home saw which sites that Z equals V over on where eyes the current. And that is the variable we are hoping to solve for. And also we&#x27;re given that Z equals 1.5 plus eight. And that V equals 1.6. Monastery 0.3. So moving right along to step number three. Um, after rearranging the equation, we have that out of the current, which we&#x27;re hoping to solve for is equal to 1.6 Monastery three I divided by 1.5 plus eight. Now we&#x27;re going to need to multiply both the numerator and the denominator of this fraction by the complex conjure git of the denominator. Okay. And that is actually 1.5 minus eight up. So we will need to foil both the numerator and denominator. Moving on to step for these calculations have been performed. Um, 1.6 times. 1.5 is 2.4 on our outer terms. Multiply. They&#x27;re going to give us monastery 0.8, uh, and moving right along, Uh, and the same processes follow for the denominator, which is shown. Okay, so we have an odd squared in both the numerator and denominator. So that is going to make, um, this plus 2.4 square into modest into modest 2.4. Because ah, square, discourage of negative one squared, which will turn the plus 2.42 minus 2.4. And lock wasn&#x27;t the denominator. We have negative 64 r squared, which is negative. 64 times negative. One amount of 64 in the plus 64. So now we have our current is equal to 2.4 modest 2.4 and the nominators. That leaves us a really component of zero. Now we have negative 12.8, and then we have the monitors of the 0.45 Um, okay, And that is going to leave us with, um mon ist 13.25 And that is going to be our imaginary component for the numerator. Now, in the denominator, we have a plus. Drove on a monastery, ola, and they&#x27;re going to cancel out. And then we have a plus 2.25 plus 64 which is 66.25 Now. Our final answer is therefore negative 13.25 divided by 66.25 I we can simplify this further using a calculator, and we will rob a final answer of negative 0.2 ah as our current or very.

Problem

Find the current that will flow when $V=1.6-0.3 i…

Problem 61 Hard Difficulty

Answer

$i^{2}=-1$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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$i^{2}=-1$

Algebra 2 and Trigonometry

Catherine R.

Alayna H.

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Absolute Value - Example 1

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Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Alayna H.

Caleb E.

Maria G.

Ann Xavier Gantert

Algebra 2 and Trigonometry