# Electromagnetic Theory Questions and Answers – Loss Tangent

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This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Loss Tangent”.

1. The loss tangent refers to the
a) Power due to propagation in conductor to that in dielectric
b) Power loss
c) Current loss
d) Charge loss

Explanation: The loss tangent is the tangent angle formed by the plot of conduction current density vs displacement current density. It is the ratio of Jc by Jd. It represents the loss of power due to propagation in a dielectric, when compared to that in a conductor.

2. Calculate the conduction current density when the resistivity of a material with an electric field of 5 units is 4.5 units.
a) 22.5
b) 4.5/5
c) 5/4.5
d) 9.5

Explanation: The conduction current density is the product of the conductivity and the electric field. The resistivity is the reciprocal of the conductivity. Thus the required formula is Jc = σ E = E/ρ = 5/4.5 units.

3. At high frequencies, which parameter is significant?
a) Conduction current
b) Displacement current
c) Attenuation constant
d) Phase constant

Explanation: The conduction current occurs in metals and is independent of the frequency. The attenuation and phase constant highly depend on the varying frequency. The displacement current occurs due to dielectrics and is significant only at very high frequencies.
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4. Find the loss tangent of a material with conduction current density of 5 units and displacement current density of 10 units.
a) 2
b) 0.5
c) 5
d) 10

Explanation: The loss tangent is the ratio of Jc by Jd. On substituting for Jc = 5 and Jd = 10, the loss tangent, tan δ = 5/10 = 0.5. It is to be noted that it is tangent angle, so that the maxima and minima lies between 1 and -1 respectively.

5. The loss tangent is also referred to as
a) Attenuation
b) Propagation
c) Dissipation factor
d) Polarization

Explanation: The loss tangent is the measure of the loss of power due to propagation in a dielectric, when compared to that in a conductor. Hence it is also referred to as dissipation factor.

6. The loss tangent of a wave propagation with an intrinsic angle of 20 degree is
a) Tan 20
b) Tan 40
c) Tan 60
d) Tan 80

Explanation: The angle of the loss tangent δ is twice the intrinsic angle θn. Thus tan δ = tan 2θn = tan 2(20) = tan 40.

7. The expression for the loss tangent is given by
a) σ/ωε
b) ωε/σ
c) σ/ω
d) ω/ε

Explanation: The conduction current density is Jc = σ E and the displacement current density is Jd = jωεE. Its magnitude will be ωεE. Thus the loss tangent tan δ = Jc /Jd = σ/ωε is the required expression.

8. Find the loss angle in degrees when the loss tangent is 1.
a) 0
b) 30
c) 45
d) 90

Explanation: The loss tangent is tan δ, where δ is the loss angle. Given that loss tangent tan δ = 1. Thus we get δ = tan-1(1) = 450.

9. The complex permittivity is given by 2-j. Find the loss tangent.
a) 1/2
b) -1/2
c) 2
d) -2

Explanation: The loss tangent for a given complex permittivity of ε = ε’ – jε’’ is given by tan δ = ε’’/ ε’. Thus the loss tangent is 1/2.

10. The intrinsic angle of the wave with a loss angle of 60 is
a) 120
b) 60
c) 90
d) 30

Explanation: The angle of the loss tangent δ is twice the intrinsic angle θn. Thus tan δ = tan 2θn. We get θn = δ/2 = 60/2 = 30 degrees.

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