Transistor load and saturation problem

[septentriones]

Homework Statement

consider the following circuit:

a) Determine the value of the resistor, R so that a current of 0.5 A flows through the load.
b) What is the maximum value of th load resistor?
c) If the load resistor is 10Ω, what value of V_B will put the transistor into saturation?

Homework Equations

I_C ≈ I_E = V_E/R_E

I_C ≈ (V_B-0.6V)/R_E

I_CR_L+V_CE+V_E=V_cc

The Attempt at a Solution

a) 0.5 ≈ (3.2 - 0.6)/R_E
R_E = 5.2Ω

b) (I am guessing that the V_CE is 0.6 V here but I am not sure)
0.5R_L+0.6+0.5 = 15
R_L = 27.8Ω

c) From what I can tell, the transistor is an NPN and in that case, in order to saturate it, the base voltage must be greater than the collector or emitters'.

V_C=I_CR_C
V_C=(0.5)(27.8)=13.9V

V_E=I_ER_E
V_E=(0.5)(5.2)=2.6V

So in order to be greater than both the V_B must be greater than 13.9V

Parts b and c I was not so sure about, thanks for any input.
(Sorry that the image is not nicely sized, I'm not sure how to fix it.)

 

[rude man]

a) is right.
b): where does the 0.5 come from? Fact: Ve + Vce + iRL = 15. You have Ve already (= iR). You can increase the load R until saturation, Vc = Vb. You know Vb so go for it.

c) Yes, saturation is when Vb = Vc. So let the load resistor = 10 ohms; then how high must Vb be to get Vc = Vb?