The correct option is C RC circuit with R=1 kΩ and C=10 μF
No information is given about leading or lagging quantity between emf and current. So, the circuit can be RC or RL.
Now, ω=100 rad/s
As,
tanϕ=XR
Here, X can be either XC or XL
Considering R=1 kΩ, as this value is common to all options.
So, tan45∘=XR⇒R=X
∴X=1000 Ω
Now, considering XL=1000 Ω
⇒ωL=1000
⇒100×L=1000 ⇒L=10 H
Now, Considering XC=1000 Ω
So, 1ωC=1000
1100×C=1000⇒C=10−5 F=10 μF
So, the phase difference between emf and current will be 45∘ if
R=1 kΩ, L=10 H or
R=1 kΩ, C=10 μF
Hence, (D) is the correct answer.