a) [tex]60 \Omega[/tex]
The total resistance of resistors connected in series is equal to the sum of the individual resistances:
[tex]R=R_1 + R_2 + .... + R_n[/tex]
In this problem, we have two resistors connected in series:
[tex]R_1 = 15 \Omega[/tex]
[tex]R_2 = 45 \Omega[/tex]
So the total resistance of the circuit is
[tex]R=R_1 + R_2 = 15 \Omega + 45 \Omega = 60 \Omega[/tex]
b) 6.0 V
The relationship between voltage, current and resistance of a circuit is given by Ohm's law
[tex]V=RI[/tex]
where
V is the voltage
R is the total resistance
I is the current
In this circuit, we have
[tex]R=60 \Omega[/tex] is the total resistance
I = 0.1 A is the current
So, the voltage of the battery is
[tex]V=(60 \Omega)(0.1 A)=6.0 V[/tex]
