Correct Answer - Option 4 : 40°
Concept:
Deflecting torque of the PMMC meter is given as,
Td = NBAI = GI
Where,
Td = deflecting torque in N-m
B = flux density in air gap, Wb/m2
N = number of turns of the coils
A = effective area of the coil in m2
I= current passing through the meter, amperes
G = constant = NBA
The spring control provides a restoring (controlling) torque given as,
TC = Kθ (Nm)
K = spring constant (Nm/degree)
θ = angle of deflection in degree
For the final steady-state deflection condition
Td = Tc
GI = Kθ
Current I = (K/G) θ .....(1)
Calculation:
Given Deflecting torque is directly proportional to current, then the scale of the ammeter is linear and the meter is PMMC type.
Given data
I1 = 5 A, θ1 = 80°
For I1 current let the deflection be θ1
I2 = 2.5 A , θ2 = ?
For I2 current let the deflection be θ2
From equation(1),
The current passing through the ammeter is directly proportional to the deflection of the pointer
I ∝ θ
\(\frac{{{I_1}}}{{{I_2}}} = \frac{{{θ _1}}}{{{θ _2}}}\)
\(\frac{5}{{2.5}} = \frac{{80^\circ }}{{{θ _2}}}\)
θ2 = 40°