There is only one voltage VA across all components in parallel.
The current in each branch equals the voltage across the branch Ib divided by the branch resistance Rb, or Ib = VA/Rb.
Kirchhoff's current law states that the total current in a parallel circuit equals the sum of the individual branch currents. Expressed as an equation, Kirchhoff's current law is <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072988215/363997/05_03sum.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>
The equivalent resistance of parallel branches is less than the smallest branch resistance, since all the branches must take more current from the source than any one branch.
For only two parallel resistances of any value, REQ = R1R2/(R1 + R2).
For any number of equal parallel resistances, REQ is the value of one resistance divided by the number of resistances.
For the general case of any number of branches, calculate as or use the reciprocal resistance formula: <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072988215/363997/05_07sum.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (2.0K)</a>
For any number of conductances in parallel, their values are added for GT in the same way as parallel branch currents are added.
The sum of the individual values of power dissipated in parallel resistances equals the total power produced by the source.
An open circuit in one branch results in no current through that branch, but the other branches can have their normal current. However, an open circuit in the main line results in no current for any of the branches.
A short circuit has zero resistance, resulting in excessive current. When one branch is short-circuited, all parallel paths are also short-circuited. The entire current is in the short circuit and no current is in the shortcircuited branches.
The voltage across a good fuse and the voltage across a closed switch are approximately 0 V. When the fuse in the main line of a parallel circuit opens, the voltage across the fuse equals the full applied voltage. Likewise, when the switch in the main line of a parallel circuit opens, the voltage across the open switch equals the full applied voltage.
