Answers to practice exercises 345
9. T =
I
PR
10. L =
X L
2π f
11. R =
E
I
12. x = a(y − 3)
13. C =
5
9
(F − 32)
14. f =
1
2π CX C
Exercise 47 (page 87)
1. r =
S − a
S
or 1 −
a
S
2. x =
d
λ
(y + λ) or d +
yd
λ
3. f =
3F − AL
3
or f = F −
AL
3
4. D =
AB 2
5E y
5. t =
R − R 0
R 0 α
6. R 2 =
R R 1
R 1 − R
7. R =
E − e − Ir
I
or R =
E − e
I
− r
8. b =
y
4ac 2
9. x =
ay
(y 2 − b 2 )
10. L =
t 2 g
4π 2
11. u =
√
v 2 − 2as
12. R =
360 A
πθ
13. a = N 2 y − x
14. L =
√
Z 2 − R 2
2π f
, 0.080
Exercise 48 (page 89)
1. a =
x y
m − n
2. R = 4
M
π
+ r 4
3. r =
3(x + y)
(1 − x − y)
4. L =
mrCR
μ − m
5. b =
c
√
1 − a 2
6. r =
x − y
x + y
7. b =
a( p 2 − q 2 )
2( p 2 + q 2 )
8. v =
u f
u − f
, 30
9. t 2 = t 1 +
Q
mc
, 55
10. v =
2dgh
0.03L
, 0.965
11. L =
8S 2
3d
+ d, 2.725
12. C =
1
ω
ωL −
√
Z 2 − R 2
, 63.1 × 10 −6
13. 64 mm 14. λ =
5
aμ
ρCZ 4 n
2
Chapter 13
Exercise 49 (page 92)
1. x = 4, y = 2
2. x = 3, y = 4
3. x = 2, y = 1.5
4. x = 4, y = 1
5. p = 2, q = −1
6. x = 1, y = 2
7. x = 3, y = 2
8. a = 2, b = 3
9. a = 5, b = 2
10. x = 1, y = 1
11. s = 2, t = 3
12. x = 3, y = −2
13. m = 2.5, n = 0.5 14. a = 6, b = −1
15. x = 2, y = 5
16. c = 2, d = −3
Exercise 50 (page 94)
1. p = −1, q = −2
2. x = 4, y = 6
3. a = 2, b = 3
4. s = 4, t = −1
5. x = 3, y = 4
6. u = 12, v = 2
7. x = 10, y = 15
8. a = 0.30, b = 0.40
Exercise 51 (page 96)
1. x =
1
2
, y =
1
4
2. a =
1
3
, b = −
1
2
3. p =
1
4
, q =
1
5
4. x = 10, y = 5
5. c = 3, d = 4
6. r = 3, s =
1
2
7. x = 5, y = 1
3
4
8. 1
Exercise 52 (page 99)
1. a = 0.2, b = 4
2. I 1 = 6.47, I 2 = 4.62
3. u = 12, a = 4, v = 26
4. £15 500, £12 800
5. m = −0.5, c = 3
6. α = 0.00426, R 0 = 22.56 7. a = 12, b = 0.40
8. a = 4, b = 10
9. F 1 = 1.5, F 2 = −4.5
Exercise 53 (page 100)
1. x = 2, y = 1, z = 3
2. x = 2, y = −2, z = 2
3. x = 5, y = −1, z = −2 4. x = 4, y = 0, z = 3