I want to know the equivalent resistance , the flow , the tension and the developing power

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gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

Equivalent resistance:

Resistors R2 ad R3 are connected in parallel to each other. 

Equivalent resistance of R2 and R3 is given as:

1/R23 = 1/R2 + 1/R3 = (R2+R3)/R2R3

or, R23  =  (R2R3)/(R2+R3)

and R23 is in series with R1.

Therefore, equivalent resistance of the circuit is given as:

R123 = R1 + R23 = R1 + (R2R3)/(R2+R3) 

Current:

The current through R1 and R23 (equivalent resistance of R2 and R3) will be the same, as `I_1` . The current will split between R2 and R3 (values are given as I2 and I3, respectively).

further, `I_1`  = `I_2 + I_3`

Voltage:

The same voltage  will pass through R2 and R3. Also, the voltage of the battery will be split between R1 and R23 (equivalent resistance of R2 and R3). 

Power: 

Power of the circuit can be calculated as I^2R, where I is the current flowing through the circuit and R is the equivalent resistance of the circuit (calculated earlier).

Therefore, Power = `I_1^2 (R_1 + (R_2R_3)/(R_2+R_3))`

Hope this helps.

kseddy123's profile picture

kseddy123 | College Teacher | (Level 1) Assistant Educator

Posted on

In the circuit given 

The equivalent resistance is calculated as follows 

R equal= R1+ parallel resistors (R2,R3)

           = R1 + `(R2*R3)/(R2+R3)`  

As when the resistors are conneted in parallel then the equivalent resistance is equal to  `1/(R2)+ 1/(R3)= (R2*R3)/(R2+R3)`

and now in the circuit, let the total current be I total 

as the two resistors are connected in parallel the current is divided into I1 and I2 which is shown in the circuit 

so the `ITotal`  = I2 +I3

So, now we can directly calculate the power (P) by the equation 

                P = (Itotal)^2 * (Requal)

                   = `(I2+I3)^2 * (R1 + (R2*R3)/(R2+R3))`

is the total power developed

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