A galvanometer with a full-scale sensitivity of 500 microA and a coil resistance of 60 ohms is to be used to build an ammeter designed to read 7.5 A. What is the required shunt resistance?

Rs = milliA

AT full scale, 500microA is going through the meter 60 ohm, or a voltage of 30mV. That same 30mV is carrying 7.5 amps (yes, less the 500microamps). R= .030/7.5 ohms

E = 5*10^-4 * 60 = 0.03 Volts.

I1 = 7.5A. = 7500 mA.
I2 = 0.5 mA.
I3 = ?

I1 = I2+I3 = 7500mA.
0.5 + I3 = 7500.
I3 = 7499.5 mA. = 7.4995A.

Rs = E/I3 = 0.03/7.4995 = 0.0040 Ohms. =
4.0 Milliohms.

To calculate the required shunt resistance (Rs), we can use the formula:

Rs = (G * Rg) / (I - Ig)

Where:
Rs = Shunt resistance (in ohms)
G = Full-scale sensitivity of the galvanometer (in amperes per volt)
Rg = Coil resistance of the galvanometer (in ohms)
I = Desired current to be measured by the ammeter (in amperes)
Ig = Current passing through the galvanometer at full-scale sensitivity (in amperes)

Given:
G = 500 microA (or 0.5 mA)
Rg = 60 ohms
I = 7.5 A

First, we need to convert the full-scale sensitivity of the galvanometer from microamperes (μA) to amperes (A):

G = 500 microA = 500 * 10^-6 A = 0.0005 A

Next, we need to find the current passing through the galvanometer at full-scale sensitivity (Ig). This can be calculated by dividing the full-scale sensitivity (G) by the coil resistance (Rg):

Ig = G / Rg

Ig = 0.0005 A / 60 ohms
Ig = 0.00000833 A

Now, we can substitute the given values into the shunt resistance formula:

Rs = (G * Rg) / (I - Ig)
Rs = (0.0005 A * 60 ohms) / (7.5 A - 0.00000833 A)
Rs = 0.03 AΩ / 7.49999167 A
Rs ≈ 0.004 ohms

Therefore, the required shunt resistance to build the ammeter designed to read 7.5 A is approximately 0.004 ohms.