Question

In the given circuit diagram, calculate the net resistance of the circuit, and hence, find the net flow of electric current.

Answer 1

Given:

R₁​ = 10 Ω

R₂ ​= 40 Ω

R₃​ = 30 Ω

R₄ ​= 20 Ω

R₅ ​= 60 Ω

Voltage, V = 12 V

1. Calculate the equivalent resistance of the upper parallel combination:

`1/R_"upper" = 1/10 + 1/40`

`1/R_"upper" = (4 + 1)/40`

`1/R_"upper" = 5/40`

`1/R_"upper" = 1/8`

`R_"upper"` = 8 Ω

2. Calculate the equivalent resistance of the lower parallel combination:

`1/R_"lower" = 1/30 + 1/20 + 1/60`

Taking LCM = 60,

`1/R_"lower" = (2 + 3 + 1)/60`

`1/R_"lower" = 6/60`

`1/R_"lower" = 1/10`

`1/R_"lower"` = 10 Ω

3. Calculate the net resistance:

The two equivalent resistances are connected in series.

R_net ​= 8 + 10 = 18 Ω

4. Calculate the current:

Using Ohm's law,

I = `V/R`

= `12/18`

= 0.667 A