# How to calculate the p(t) of (v(t)=10V*(wt)) connected across a 2 k ohm resistor

#### Neil543

##### New member
Hello all,

I have been given this question by my lecturer and if I'm honest I don't even know where to start. Can someone please explain to me how I should approach tackling this question, explaining it in the most basic of terms?

calculate the p(t) of (v(t)=10V*(wt)) connected across a 2 k ohm resistor

Thanks
Neil

#### Otis

##### Senior Member
(v(t) = 10V*(wt))
Hello. Are you sure that's what the lecturer wrote? I'm too rusty on circuits to help, but it seems like the right-hand side ought to contain a trig function, as instantaneous power p(t) is a sinusoidal function (I believe).

PS: The grouping symbols highlighted in red are unnecessary.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello all,

I have been given this question by my lecturer and if I'm honest I don't even know where to start. Can someone please explain to me how I should approach tackling this question, explaining it in the most basic of terms?

calculate the p(t) of (v(t)=10V*(wt)) connected across a 2 k ohm resistor

Thanks
Neil
Power = current * voltage

and

Voltage = current * resistance

Now first derive the expression for power in terms of voltage and resistance.

#### Dr.Peterson

##### Elite Member
I have been given this question by my lecturer and if I'm honest I don't even know where to start. Can someone please explain to me how I should approach tackling this question, explaining it in the most basic of terms?

calculate the p(t) of (v(t)=10V*(wt)) connected across a 2 k ohm resistor
Please define the terms here. Is it true that p(t) means power, varying with time? Does the capital V just mean volts, or something else? What is wt? Is it supposed to be sin(wt) or cos(wt), where w is frequency?

We need to see what you have been taught, with which the question can be answered.

#### Neil543

##### New member
Hello. Are you sure that's what the lecturer wrote? I'm too rusty on circuits to help, but it seems like the right-hand side ought to contain a trig
Hello all,

I have been given this question by my lecturer and if I'm honest I don't even know where to start. Can someone please explain to me how I should approach tackling this question, explaining it in the most basic of terms?

calculate the p(t) of (v(t)=12V*(wt)) connected across a 5 k ohm resistor

Thanks
Neil
function, as instantaneous power p(t) is a sinusoidal function (I believe).

PS: The grouping symbols highlighted in red are unnecessary.

Yes, but I may have omitted some important info through ignorance more than intention. If it is ok I am going to change the formula slightly so that with all of your help I will be able to answer the original in the future on my own.

Here is the new equation including the full question...

A sinusoidal voltage source (v(t)=12V*sin(wt) is connected across a 5k ohm resistor.

1) make a sketch of the p(t), the instantaneous power supplied by the source

#### Subhotosh Khan

##### Super Moderator
Staff member
Yes, but I may have omitted some important info through ignorance more than intention. If it is ok I am going to change the formula slightly so that with all of your help I will be able to answer the original in the future on my own.

Here is the new equation including the full question...

A sinusoidal voltage source (v(t)=12V*sin(wt) is connected across a 5k ohm resistor.

1) make a sketch of the p(t), the instantaneous power supplied by the source
To repeat response #2:

Power = current * voltage

and

Voltage = current * resistance

Now first derive the expression for power as a function of voltage and resistance.

#### Neil543

##### New member
To repeat response #2:

Power = current * voltage

and

Voltage = current * resistance

Now first derive the expression for power as a function of voltage and resistance.

Hello,

I'm running the risk of sounding a complete idiot here but what do you mean by "Now first derive the expression for power as a function of voltage and resistance"?

so far I have calculated that

1. Current (I)= 2.4A (V/R=I)
2. Power (P) = 28.8W (I*V=P)
3. Volt (V) = 12v (provided)
4. Resistance (R) = 5 ohm (provided)

Neil

#### Neil543

##### New member
Please define the terms here. Is it true that p(t) means power, varying with time? Does the capital V just mean volts, or something else? What is wt? Is it supposed to be sin(wt) or cos(wt), where w is frequency?

We need to see what you have been taught, with which the question can be answered.
Hello,

My understanding is that p(t) means instantaneous power and yes I assume that V just means volts. I have had to google this a few times as V and v pop-up all over the place.

In regards to the sin or cos question, I have no idea.

#### Neil543

##### New member
Please define the terms here. Is it true that p(t) means power, varying with time? Does the capital V just mean volts, or something else? What is wt? Is it supposed to be sin(wt) or cos(wt), where w is frequency?

We need to see what you have been taught, with which the question can be answered.
Hello again,

Sorry for the miss-information, I made a mistake in the equation it is supposed to be: (v(t)=12V*sin(wt)) connected across a 5K ohm resistor.

#### Dr.Peterson

##### Elite Member
Yes, but I may have omitted some important info through ignorance more than intention. If it is ok I am going to change the formula slightly so that with all of your help I will be able to answer the original in the future on my own.

Here is the new equation including the full question...

A sinusoidal voltage source (v(t)=12V*sin(wt) is connected across a 5k ohm resistor.

1) make a sketch of the p(t), the instantaneous power supplied by the source
Thanks for providing the actual question. I'm not sure how "ignorance" would lead to entirely dropping "sin", but we can more on.

The "sin" is what it means to be a "sinusoidal voltage source". I wouldn't have put V for volts in the middle of an expression, but I guess we have to assume it means v(t) = 12sin(wt), where t is time (in seconds?) and w (actually the Greek letter omega, ω) is the frequency.

The next question we need to ask is, what do you know about this subject? I see you are familiar with facts like P = VI and V = IR, which Khan referred to a couple times. But what do you know about sinusoidal functions? We really need to know what we can expect you to understand, in order to help.
so far I have calculated that

1. Current (I)= 2.4A (V/R=I)
2. Power (P) = 28.8W (I*V=P)
3. Volt (V) = 12v (provided)
4. Resistance (R) = 5 ohm (provided)
The trouble here is that, unless I'm reading something wrong, you are not told that the voltage is a constant 12 V; that's the point of calling it sinusoidal. So you appear to be ignoring the main point of the problem. On the other hand, there's not much more to do.

What is the context of the question?

#### Neil543

##### New member
Thanks for providing the actual question. I'm not sure how "ignorance" would lead to entirely dropping "sin", but we can more on.

The "sin" is what it means to be a "sinusoidal voltage source". I wouldn't have put V for volts in the middle of an expression, but I guess we have to assume it means v(t) = 12sin(wt), where t is time (in seconds?) and w (actually the Greek letter omega, ω) is the frequency.

The next question we need to ask is, what do you know about this subject? I see you are familiar with facts like P = VI and V = IR, which Khan referred to a couple times. But what do you know about sinusoidal functions? We really need to know what we can expect you to understand, in order to help.

The trouble here is that, unless I'm reading something wrong, you are not told that the voltage is a constant 12 V; that's the point of calling it sinusoidal. So you appear to be ignoring the main point of the problem. On the other hand, there's not much more to do.

What is the context of the question?
I know the very basics, ohms law and some other basic electronic principles. I have no experience of sinusoidal functions.

I would like to understand what I'm looking at, at the very core of it. For example, if I have a 12v sinusoidal power supply: is there a standard calculation that I can apply to work out the wave forms peak and trough? If someone could break it into its constituent steps, noting what the rules/laws are that are involved, I could then use that guidance to build on my own knowledge.

Thank you
Neil

#### Subhotosh Khan

##### Super Moderator
Staff member
I know the very basics, ohms law and some other basic electronic principles. I have no experience of sinusoidal functions.

I would like to understand what I'm looking at, at the very core of it. For example, if I have a 12v sinusoidal power supply: is there a standard calculation that I can apply to work out the wave forms peak and trough? If someone could break it into its constituent steps, noting what the rules/laws are that are involved, I could then use that guidance to build on my own knowledge.

Thank you
Neil
In which class were you assigned this problem - mathematics or physics or engineering? Or you are doing a self-study tour?

#### Otis

##### Senior Member
Please double-check the impedance of the resistor. You wrote 2k ohms twice and 5k ohms twice.

#### Neil543

##### New member

Please double-check the impedance of the resistor. You wrote 2k ohms twice and 5k ohms twice.

The question that I have been set is 2k ohms, I've changed it to 5k ohms as I don't want to answer my question through this group I want to learn how to answer it. Sorry for the confusion.

#### Neil543

##### New member
In which class were you assigned this problem - mathematics or physics or engineering? Or you are doing a self-study tour?
Engineering, specifically electronic circuit interrogation.

#### Subhotosh Khan

##### Super Moderator
Staff member
P = I * V = (V/R) * V = V2/R

Does that help?

When you are saying V =12 and V is a sine function:
• Do you mean the amplitude of the Voltage function is 12, or
• Do you mean the RMS (root-mean-square) of the Voltage function is 12, or
• something else,,,
You are saying this is a problem from an engineering class. You should have come across functions like sin(x) or cos(x) in your physics class (prereq for most of the engineering classes).

#### LCKurtz

##### Junior Member
The fact that your input voltage is sinusoidal suggests your course is about to introduce circuits with reactive loads. If you are telling us the voltage is $$\displaystyle 12$$ when it is actually $$\displaystyle 12\sin(\omega t)$$ because you don't understand the difference, you are going to quickly be in over your head.

#### Otis

##### Senior Member
… I have no experience [with] sinusoidal functions …
Then you ought to learn the basics of trigonometry, before studying circuits.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello all,

I have been given this question by my lecturer and if I'm honest I don't even know where to start. Can someone please explain to me how I should approach tackling this question, explaining it in the most basic of terms?

calculate the p(t) of (v(t)=10V*sin(wt)) connected across a 2 k ohm resistor Thanks Neil
Enough time has passed since problem was posted.

I am still not clear about "math pre-req" in your class. In an engineering class, I would expect following response:

p(t) = [v(t)]^2 / R = 50 * sin2(wt) = 25*[1 - cos(2wt)] watts

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