46. Four possibilities exist: (1) C

1

= 4.00 µF is used alone; (2) C

2

= 6.00 µF is used alone; (3) C

1

and C

2

are

connected in series; and (4) C

1

and C

2

are connected in parallel. The corresponding resonant frequencies

are

f

1

=

1

2π

√

LC

1

=

1

2π

(2.00

× 10

−3

H)(4.00

× 10

−6

F)

= 1.78

× 10

3

Hz

f

2

=

1

2π

√

LC

2

=

1

2π

(2.00

× 10

−3

H)(6.00

× 10

−6

F)

= 1.45

× 10

3

Hz

f

3

=

1

2π

LC

1

C

2

/(C

1

+ C

2

)

= 2.30

× 10

3

Hz

f

4

=

1

2π

L(C

1

+ C

2

)

= 1.13

× 10

3

Hz .