# Finding maximal total current for a system

1. Feb 21, 2014

### Phys student

1. The problem statement, all variables and given/known data

a) There are two fuses connected in parallel: fuse A has resistance R_A = 1Ω and
maximal current (by which it melts) I_Amax = 1A; fuse B
has resistance R_B = 2Ω and maximal current (by which it
melts) IBmax = 1.2A. What is the maximal total current for
such a system of fuses?

b) What is the total current when the
fuse B is substituted with a fuse C which has R_C = 2Ω and
I_Cmax = 1.7A?

3. The attempt at a solution

for part (a) we have:

$$R_B/R_A = I_A/I_B = 2$$ because of that fuse A will melt first (the current through it will be 1 A) so we substitute it in the equation and solve for I_B, we get:

$$I_B = 0.5 A$$

So:

$$I = 0.5+1 = 1.5 A$$

I'm not sure how to do part B

Edit: Answers are: a) 1.5 A
b) 1.7 A

2. Feb 21, 2014

### haruspex

Looks like a mistake in the question to me. Are you sure you've quoted it correctly?

3. Feb 22, 2014

### Phys student

Yes, I'm sure.

4. Feb 22, 2014

### voko

Imagine in part (B) current exceeds 1.5 A. What happens then?

5. Feb 22, 2014

### Phys student

Then fuse A would burn and the current would be redirected to fuse C only?

6. Feb 22, 2014

### voko

Correct.

7. Feb 22, 2014

### Phys student

So the answer is 1.7A because after changing to fuse C a larger maximal current is possible where fuse A would burn and the current (1.7A) would be redirected to fuse C only.

8. Feb 22, 2014

### voko

1.7 A is possible from the beginning, it is just that fuse A gets blown in the process. This is different from case (a), where the max current is only possible with the two fuses intact.

9. Feb 22, 2014

Doh!