Resistance in Parallel Formula

There are two major ways of connecting resistances in an electric circuit. Either they can be connected in parallel, or they can be connected in series. In this article we shall see connection of resistances in parallel circuit. Understanding Examples of Gravitational Potential Energy is always challenging for me but thanks to all math help websites to help me out.

Introduction to Resistance in Parallel Formula

When we apply a potential difference between two ends of a conductor, an electric field will be set up inside the conductor and as a result current flows through the conductor. The applied potential difference is proportional to the current flowing in the conductor. If V is the potential difference applied and I is the current then V α I Or V = RI Here R is the constant of proportionality called resistance.

Resistors in Parallel Formula: Definition of Resistance

Resistance is characteristic of the material of the conductor. Resistance is given by the equation

R = V / I

Units: Volts / ampere or ohms (Ω)

The value of resistance of a conductor depends upon (a) nature of the material, (b) its dimensions (length & cross section area), (c) temperature of the conductor. At constant temperature, the resistance (R) of a wire is directly proportional to the length (L) of the wire and inversely proportional to area (A) of cross section.

R α L

and R α (1 /A)

So R α (L / A)

Or R = ρ (L / A). Here ρ is called the constant of proportionality termed as specific resistance or resistivity. Resistivity is specific property of material of the conductor which is independent of physical parameters of the conductor. Is this topic Physics Power Equation hard for you? Watch out for my coming posts.

Formula for Resistors in Parallel

When two resistors of resistance R1 & R2 are connected in parallel to the battery then the voltage across each resistor remains the same and the total current is sum of the current flowing in each branch of the circuit The Voltage across each resistor is V and the Current in the circuit is I. This current is broken as I1 & I2 in the branch circuits respectively. The total current is the sum of currents in the branch circuits. `I = I_1 + I_2`. From Ohms law the current is

`I_1 = V/ R_1` and `I_2 = V /R_2` .

If `R_e` is the total resistance offered by the circuit due to the parallel combination then `I = V /R_e` .

Substituting the current values in the above equation

` V /R_e = V/ R_1 + V/R_2 `

`=>( V /R_e ) = V [( 1/ R_1 ) + ( 1 /R_2 )] `

`=>( 1 /R_e ) = ( 1/ R_1 ) + ( 1 /R_2 ) `

`=>R_e =` `( R_1 R_2) / (R1+ R2)` This is the required equation for resistors connected in parallel.