an ammeter of resistance 0.1ohms has a full scale deflection of 50mA .
Determine the resultant full scale deflection of the meter when a shunt of 0.0111 ohms is connected across its terminals?
Im = 50 mA = 0.05 A = Current through meter.
Ir = 0.10/0.0111 * 0.05A = 0.450A = Current through resistor.
Im + Ir = 0.05 + 0.450 = 0.500A = Full-scale reading.
To determine the resultant full-scale deflection of the meter when a shunt of 0.0111 ohms is connected across its terminals, we can use the formula relating the resistance of the shunt to the fractional change in current.
The formula is:
\(R_s = \frac{R_m}{I_{m_fsd} - I_{s_fsd}}\)
Where:
- \(R_s\) is the resistance of the shunt
- \(R_m\) is the resistance of the ammeter
- \(I_{m_fsd}\) is the full-scale deflection current of the ammeter
- \(I_{s_fsd}\) is the desired full-scale deflection current
In this case, the resistance of the ammeter is given as 0.1 ohms, and the full-scale deflection current of the ammeter is 50 mA (or 0.05 A).
Plugging these values into the formula, we get:
\(0.0111 = \frac{0.1}{0.05 - I_{s_fsd}}\)
Now, we can solve this equation for \(I_{s_fsd}\):
\(0.0111(0.05 - I_{s_fsd}) = 0.1\)
\(0.000555 - 0.0111I_{s_fsd} = 0.1\)
\(0.0111I_{s_fsd} = 0.000555 - 0.1\)
\(0.0111I_{s_fsd} = -0.099445\)
\(I_{s_fsd} = \frac{-0.099445}{0.0111}\)
\(I_{s_fsd} \approx -8.953 mA\)
Therefore, the resultant full-scale deflection of the meter when a shunt of 0.0111 ohms is connected across its terminals is approximately -8.953 mA.
To determine the resultant full scale deflection of the meter when a shunt of 0.0111 ohms is connected across its terminals, we can use the principle of parallel resistance.
First, let's calculate the resistance of the combination of the ammeter and the shunt when they are connected in parallel. The formula to calculate the total resistance in a parallel circuit is:
1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
In this case, we have two resistors in parallel: the resistance of the ammeter (R1 = 0.1 ohms) and the shunt (R2 = 0.0111 ohms):
1/R_total = 1/0.1 + 1/0.0111
Simplifying this equation gives us:
1/R_total = 10 + 90.09
1/R_total = 100.09
Now we can find the value of R_total by taking the reciprocal of both sides:
R_total = 1/100.09
R_total = 0.00999 ohms (approximately)
Next, we can calculate the current passing through the combination of the ammeter and the shunt by using Ohm's Law:
I = V / R
The voltage across both the ammeter and the shunt is the same, and it is equal to the full scale deflection of the ammeter, which is 50mA (or 0.05A). The total resistance in this combination is R_total = 0.00999 ohms, as we calculated earlier:
I = 0.05 / 0.00999
I ≈ 5.005 A
Therefore, the resultant full scale deflection of the meter when a shunt of 0.0111 ohms is connected across its terminals is approximately 5.005 A.
voltage across meter for full scale: I*R=.1*.050=.005 volts
total current under .005 volts with .1 in parallel with .0111
...resistance= 1/R=1/.1 + 1/.0111
R= .00111/(.1111)=.0100ohms
full scale reading with then be at V/R=. .05//01 =5 amps
check my work.