What is the current I shown in the given circuit?

Options

A. `(V )/(2R)`
B. `(V )/(R )`
C. `(V )/(16 R)`
D. `(V )/(8R)`

Answer

C

Explanation

The equivalent circuit diagram is as follows

In loop 4 we get ` R_1 = (2 R xx 2R )/(2R + 2R) = R `
In loop 3, we get ` R_2 = ((R+ R_1)xx 2 R)/(2 R +(R +R_1))=R `
In loop 2 we get ` R_3 = ((R +R_2)xx 2 R)/( 2 R +(R + R_2))=R`
In loop 1 , we get ` R_4 = R + R_3 = R+ R = 2R `
` therefore I =(I_1)/( 8 ) = (V //2 R) /(8 ) = (V )/( 16 R )`