Answer:
10.15Ω
Explanation:
From ohm's law,
V = IR...................... Equation 1
Where V = Voltage, I = current, R = resistance.
Assume the voltage across the resistance = V,
Given: I = 6.3 A
Substitute into equation 1
V = 6.3R.................. Equation 2
When an additional resistance of 3.4 Ω is inserted in series with R,
The voltage remain the same, but the current changes
Total Resistance(Rt) = (R+3.4)Ω, I' = 4.72 A
Also from ohm' law,
V = I'Rt............... Equation 3
Substitute the value of I' and Rt into equation 3
V = 4.72(R+3.4)............... Equation 5.
Divide equation 2 by equation 5
V/V = 6.3R/4.72(R+3.4)
1 = 1.335R/(R+3.4)
1 = 1.335R/(R+3.4)
R+3.4 = 1.335R
3.4 = 1.335R-R
3.4 = 0.335R
R = 3.4/0.335
R = 10.15Ω
