# brief explanation of Ohm's law

How can I calculate ideal values of current for both short and open circuits by using Ohm's law. Further more usually said that it is not advisable to connect DC batteries of different voltages in parallel can you explain it for me in the light of Ohm's law?

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A short circuit is an abnormal connection between two nodes of an electric circuit intended to be at different voltages. This results in an excessive electric current limited only by the Thévenin equivalent resistance of the rest of the network and potentially causes circuit damage, overheating, fire or explosion. Although usually the result of a fault, there are cases where short circuits are caused intentionally, for example, for the purpose of voltage-sensing crowbar circuit protectors. while an open electric circuit through which current cannot flow because the path is broken or interrupted by an opening.

• What do you know about short circuits and open circuits? What is the resistance of a short circuit? What is the resistance of an open circuit? – Greg d'Eon Apr 11 '15 at 13:50

Assuming that ideal short has a resistance of $0$ ohms (so infinite conductance $G_{open}=\infty$) and ideal open circuit has infinite resistance (so zero conductance $G_{short}=0$) and voltage of ideal source is greater than 0:

$$I_{short} = G_{short} \cdot U = \infty \cdot U = \infty A$$ $$I_{open} = G_{open} \cdot U = 0 \cdot U = 0 A$$

Look for this simple circuit with two batteries with different voltages, connected in parallel with ideal zero ohm wires, so they have infinite conductance. We assume that battery is an ideal voltage source, without internal resistance.

simulate this circuit – Schematic created using CircuitLab

Potential of node V1 is 2V and potential of node V2 is 4V, so voltage between V1 and V2 is: $$U_{V1,V2} = U_{V2} - U_{V1} = 4 - 2 = 2V$$ and then the current flowing through the ideal wire is: $$I_{wire} = U_{V1,V2} \cdot G_{wire} = 2 \cdot \infty = \infty A$$

Of course, for above example we assume that every element in a circuit is ideal. In real circuits they are not, batteries has internal resistance from hundreds of ohms (for small button cells) to several ohms (for big car batteries), wires and connections has resistance of miliohms to ohms. So short current never be infinite, but may be very huge and destroy elements thermally.

If you connect two batteries of different voltages in parallel, Ohm's Law says the current will be (Va-Vb)/0. In practice, the current will be somewhat less than that calculation would indicate, due to internal resistance of the batteries, and the non-zero resistance of real wires, however, the current will still be unacceptably large.

• but what will be the advantage or disadvantage to connect it in parallel way – Mubeen Raza Rashid Apr 12 '15 at 6:56
• You do not ever connect sources of different voltages directly in parallel. That would cause hugh currents to flow between the sources. If the two sources were batteries, the higher voltage one would be quickly discharged, and possibly damaged by the high current, while the lower voltage battery will be damaged by the reverse current forced into it by the higher voltage battery. – Peter Bennett Apr 12 '15 at 16:38