This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values. The resistance of the moving-coil instrument is R_m = 5 \, . The full-scale deflection current of the instrument is I_m = 20 \, mA = 0.020 \, A. The total current to be measured is I = 3 \, A. Step 2: Determine the current that must flow through the shunt resistor. When a shunt resistor is connected in parallel with the instrument, the total current I splits between the instrument current I_m and the shunt current I_sh. I = I_m + I_sh Therefore, the current through the shunt resistor is: I_sh = I - I_m I_sh = 3 \, A - 0.020 \, A I_sh = 2.98 \, A Step 3: Calculate the voltage across the instrument. Since the shunt resistor is in parallel with the instrument, the voltage across both components is the same. The voltage across the instrument is: V_m = I_m × R_m V_m = 0.020 \, A × 5 \, V_m = 0.1 \, V Step 4: Calculate the shunt resistance. The voltage across the shunt resistor is equal to the voltage across the instrument, V_sh = V_m = 0.1 \, V. Using Ohm's Law for the shunt resistor: V_sh = I_sh × R_sh R_sh = V_shI_sh R_sh = 0.1 \, V2.98 \, A R_sh ≈ 0.033557 \, Step 5: Round the final answer. R_sh ≈ 0.0336 \, The shunt resistance required is 0.0336 .