A moving coil galvanometer has a resistance of 4 ohms and gives full-scale deflection when carrying 30 milliamperes. The instruments can be used to measure 150 volts by connecting in series with the instrument a resistance of
The full-scale deflection current of the moving coil galvanometer is 30 milliamperes. Let's assume that the resistance of the galvanometer is connected in series with the resistance Rs.
The current through the circuit when measuring 150 volts is given by:
I = V / (Rs + Rg)
where V is the voltage being measured, Rs is the added series resistance, and Rg is the resistance of the galvanometer.
At full-scale deflection, I = 30 mA, and the voltage drop across the galvanometer is:
Vg = I * Rg = 0.03 A * 4 Ω = 0.12 V
The remaining voltage drop is across the series resistance Rs:
Vr = V - Vg = 150 V - 0.12 V = 149.88 V
Using Ohm's law, we can solve for the required series resistance Rs:
Rs = Vr / I = 149.88 V / 0.03 A = 4996 Ω
Therefore, the resistance that should be connected in series with the moving coil galvanometer is 4996 ohms.