Given that the voltage accross the battery is V = 7.0 V
when the resistances are in parallel the the current through the resister B is IB = 3.0 A
when the resisters are in seires then the voltage accross the resester A is VA = 4.0 V
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if the resistances are in parallel then the
current flowing through the resisr\ters Ia = I*RB / (RA+RB)
3.0 A = I*RB / (RA+RB) ---------(1)
the resultant resistance is R = RA *RB / (RA+RB)
current is I = V / R
= 7.0V *(R
A+RB)/ R
A *R
B ----------------(2)
from the equations (1) and (2) we get
3.0A = 7.0 V / RB
RB = 7.0 V / 3.0A = 2.33 Ω
if the resisters are in seires then voltage accross the resester A is
VA = V*RA / (RA+RB)
4.0V = 7.0V * RA / (RA+RB)
RA / (RA+RB) = 4.0V/ 7.0V ----------(3)
substitude the value of RB in equation (3) we get value of RA = -------- Ω