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
To convert a galvanometer into an ammeter, a low resistance resistor, called a shunt resistor, is connected in parallel with the galvanometer. Step 1: Identify the given values. Galvanometer full-scale deflection current, I_g = 10 \, mA = 10 × 10^-3 \, A = 0.01 \, A Galvanometer coil resistance, R_g = 30 \, Desired ammeter range (total current), I = 10 \, A Step 2: Determine the current through the shunt resistor. When the galvanometer and shunt resistor are in parallel, the total current I splits between them. The current through the shunt resistor, I_sh, is given by: I_sh = I - I_g I_sh = 10 \, A - 0.01 \, A I_sh = 9.99 \, A Step 3: Calculate the voltage across the galvanometer. The voltage across the galvanometer at full-scale deflection is: V_g = I_g R_g V_g = (0.01 \, A)(30 \, ) V_g = 0.3 \, V Step 4: Calculate the shunt resistance. Since the galvanometer and the shunt resistor are in parallel, the voltage across them is the same (V_g = V_sh). V_sh = I_sh R_sh Therefore, R_sh = V_shI_sh = (V_g)/(I_sh) R_sh = 0.3 \, V9.99 \, A R_sh ≈ 0.03003 \, Step 5: Choose the correct option. The calculated shunt resistance is approximately 0.03 \, . Since it must be a shunt resistor (connected in parallel), the correct option is B. The final answer is B. 0.03 shunt resistor