i'm reading the books about the basic electirc thoery.
and when i learn the OHM's law,and Kirchhoff's law
i design a circuit V1=V2=V3)
we know that V1/R=i1+i2
and what makes me confused is the value of i1 and i2 respectively??
(i2 is the current through the short circuit,and the voltage resuorce is ideal...)
i think it is hard to determinate the current i1 and i2.......
would someone give me a detailed explanation,thanks !

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as u know the current thru the R will have no i2 component when dealing with V1 only , since the v2 and v3 are considered short ckt.

here u need to apply the superposition theorem , calculate I1 with V1 , V2 and V3 shorted out, then calculate I23 with V2, V3 and V1 shorted
and add the currents

don't forget the current directions..

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Since V2 = V3 there will be no current due to these sources so you can remove them from the circuit, assuming that they have no internal resistance.

Now you have 2 wires in parallel. If you assume that these wires have no resistance, then I2 cannot be calculated. All you can do is remove one wire and calculate I1, ie. I1 = V1/R.

But if the wires do have resistance, then you can use Ohm's and Kirchoff's laws to calculate both I1 & I2.

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Len

 

In that case we really can't get the current i1 and i2 under ideal conditon????

 

Since V3 = V2, the sum is zero and there is no current I1. Therefore, I2 = V1/R.

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No, the currents I1 & I2 are both indeterminant since V2 + V3 = 0 and assuming that there is no resistance in the wires, then

I1 = 0/0 and I2 = 0/0

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Len

 

ohh.. i missed the opposing v2 and v3.. yes in ideal case there will be only i1

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[quote=akg]No, as I explained above, I1 and I2 are indeterminant.

The only current you can calculate is the one through the resistor.

However, in practice, the wires would have some resistance and therefore the currents could be calculated.

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Len

 

yes i got it 0/0~~~~
it's indeterminant~~~~~~~~~~~ :wink:

 

Yes.
Another way to look at it is that the sum I1 + I2 can be determined.

I1 + I2 = V/R. So if we let V = 10 Volt and R = 10 Ohm, then

I1 + I2 = 1 Amp. Thus I2 = 1 - I1.

But there is an infinite number of solutions to this equation since there are an infinite number of possible values for I1 and therefore an infinite number of corresponding values for I2.

For example, if I1 = 0.65 Amp, I2 = 0.35 Amp.

Or if I1 = 0.299 Amp, I2 = 0.701 Amp, etc.

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Len

 

Be careful with you upper and lower case, V is DC voltage or rms, p-p AC, v is instantaneous voltage and the same goes for current.

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YES,maybe we could get the result from the picture below......

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