Show that the voltage across resistor R2

In summary, the voltage across resistor R2 in the given circuit can be determined using the fact that the total power supplied is equal to the total power absorbed. This leads to the equation v_{R_{2}} = v_{s}\frac{R_{2}}{R_{1} + R_{2}}. Applying Ohm's law, the total resistance in the circuit can be found by dividing the voltage by the current, and the current can be found by dividing the voltage by the total resistance. Finally, the voltage across R2 can be calculated using the equation mentioned earlier. The mention of power in the problem is to emphasize the absence of internal resistance in the source.
  • #1
KillerZ
116
0

Homework Statement



In the circuit shown, the same current must flow through all three componets as a result of conservation laws. Using the fact that the total power supplied equal the total power absorbed, show that the voltage across resistor R2 is given by:

[tex]v_{R_{2}} = v_{s}\frac{R_{2}}{R_{1} + R_{2}}[/tex]

2d6p6xw.png


Homework Equations



[tex]p = vi = i^{2}R = \frac{v^{2}}{R}[/tex]

The Attempt at a Solution



I said:

[tex]p_{v_{s}} = p_{R_{1}} + p_{R_{2}}[/tex]

because power supplied = power absorbed

[tex]p_{v_{s}} = p_{R_{1}} + p_{R_{2}}[/tex]

But I don't think this is right because it would not simplify right.

[tex]v_{s}i = i^{2}R_{1} + \frac{v_{R_{2}}^{2}}{R_{2}}[/tex]
 
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  • #2


Since total power supplied is equal to the total power absorbed, there is no internal resistance in Vs.
Apply the ohm's law to the circuit and find VR2.
 
  • #3


I am still having trouble with this.

I know Ohm's law is

[tex]v = IR[/tex]

[tex]I = \frac{v}{R}[/tex]

and

[tex]R = \frac{v}{I}[/tex]

but do I just just use them with this:

[tex]p_{v_{s}} = p_{R_{1}} + p_{R_{2}}[/tex]

[tex]v_{s}i = i^{2}R_{1} + \frac{v_{R_{2}}^{2}}{R_{2}}[/tex]
 
  • #4


What is the total resistance in the circuit?
What is the current in the circuit?
And then what is the voltage across R2?
Here you need not use the power formula.
In the problem the mention of the power is to emphasis the absence of internal resistance in the source.
 

1. How do you calculate the voltage across resistor R2?

The voltage across resistor R2 can be calculated using Ohm's Law, where V is the voltage, I is the current, and R is the resistance. The formula is V = I * R.

2. What is the purpose of calculating the voltage across resistor R2?

Calculating the voltage across resistor R2 allows us to understand the flow of electricity through a circuit. It helps us determine the amount of voltage drop across the resistor, and how much power is being dissipated.

3. How is the voltage across resistor R2 affected by changes in current or resistance?

The voltage across resistor R2 is directly proportional to the current, meaning that if the current increases, the voltage will also increase. However, it is inversely proportional to the resistance, meaning that if the resistance increases, the voltage will decrease.

4. Can the voltage across resistor R2 ever be greater than the voltage of the power source?

No, the voltage across resistor R2 cannot be greater than the voltage of the power source. This is because the voltage across each component in a series circuit must add up to the total voltage of the power source.

5. How can the voltage across resistor R2 be measured in a circuit?

The voltage across resistor R2 can be measured using a voltmeter, which is connected in parallel to the resistor. The voltmeter will display the voltage reading, allowing us to determine the voltage across R2.

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