48.

(a) Since L

eq

= L

1

+ L

2

and C

eq

= C

1

+ C

2

+ C

3

for the circuit, the resonant frequency is

ω

=

1

2π

L

eq

C

eq

=

1

2π

(L

1

+ L

2

)(C

1

+ C

2

+ C

3

)

=

1

2π

(1.70

× 10

−3

H + 2.30

× 10

−3

H)(4.00

× 10

−6

F + 2.50

× 10

−6

F + 3.50

× 10

−6

F)

=

796 Hz .

(b) The resonant frequency does not depend on R so it will not change as R increases.

(c) Since ω

∝ (L

1

+ L

2

)

−1/2

, it will decrease as L

1

increases.

(d) Since ω

∝ C

−1/2

eq

and C

eq

decreases as C

3

is removed, ω will increase.