Find the current i_m' in the given circuit.

The correct answer is option 2):(-1 A)

Concept:

When two resistors R1 and R2 are connected in series the total resistance 

Rt = R1 +R2

When two resistors R1 and R2 are connected in parallel the total resistance will be

Rt = (\(1\over R_1\) + \(1\over R_2\))-1

Current Division method

Current through R1 \(I_1=I×\frac{R_2}{R_1+R_2}\)

Current through R2 \(I_2=I×\frac{R_1}{R_1+R_2}\)

By  ohms law 

V = IR 

where I is the current R is the resistor

Calculation:

The given circuit is 

Current through R2 \(I_2=I×\frac{R_1}{R_1+R_2}\)

= 5 × \(10\over 50\)

= 1 A

the direction of the current is reversed so I_m = -1 A