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
Huu ni tatizo kuhusu kipimo cha koili inayohamia (moving coil instrument) kinachotumika kama voltmeter, na jinsi mabadiliko ya halijoto yanavyoathiri usahihi wake. Upinzani wa chombo, R_m = 25 \ Voltage ya mkengeuko kamili (full scale deflection), V_m = 25 \ mV = 0.025 \ V Kiwango cha voltage kinachohitajika, V = 10 \ V Mgawo wa halijoto wa shaba (copper), _Cu = 0.004/ \ ^C Mgawo wa halijoto wa manganin, _Mn = 0.00015/ \ ^C Ongezeko la halijoto, T = 10 \ ^C Tunahitaji kuamua kosa linalosababishwa na ongezeko la halijoto. Step 1: Kokotoa mkondo wa mkengeuko kamili (I_m) wa chombo. I_m = (V_m)/(R_m) I_m = (0.025 \ V)/(25 \ ) = 0.001 \ A = 1 \ mA Step 2: Kokotoa upinzani wa kiongezeo (multiplier resistance, R_s) unaohitajika ili kupanua kiwango cha voltage hadi 10 \ V. Kwa voltmeter, jumla ya upinzani ni R_total = (V)/(I_m). R_s = R_total - R_m = (V)/(I_m) - R_m R_s = (10 \ V)/(0.001 \ A) - 25 \ = 10000 \ - 25 \ = 9975 \ Step 3: Kokotoa upinzani mpya wa chombo (R_m') baada ya ongezeko la halijoto la 10 \ ^C. R_m' = R_m (1 + _Cu T) R_m' = 25 \ (1 + 0.004/ \ ^C × 10 \ ^C) R_m' = 25 \ (1 + 0.04) = 25 \ (1.04) = 26 \ Step 4: Kokotoa upinzani mpya wa kiongezeo (R_s') baada ya ongezeko la halijoto la 10 \ ^C. R_s' = R_s (1 + _Mn T) R_s' = 9975 \ (1 + 0.00015/ \ ^C × 10 \ ^C) R_s' = 9975 \ (1 + 0.0015) = 9975 \ (1.0015) = 9989.9625 \ Step 5: Kokotoa jumla ya upinzani mpya wa voltmeter (R_total') baada ya ongezeko la halijoto. R_total' = R_m' + R_s' R_total' = 26 \ + 9989.9625 \ = 10015.9625 \ Step 6: Kokotoa voltage mpya ya mkengeuko kamili (V') kwa mkondo uleule wa I_m. V' = I_m × R_total' V' = 0.001 \ A × 10015.9625 \ = 10.0159625 \ V Step 7: Kokotoa kosa linalosababishwa na ongezeko la halijoto. Kosa = Voltage mpya - Voltage iliyokusudiwa Kosa = V' - V Kosa = 10.0159625 \ V - 10 \ V = 0.0159625 \ V Kosa linaweza kuzungushwa hadi sehemu nne za desimali. Kosa ≈ 0.0160 \ V Kosa linalosababishwa na ongezeko la halijoto ni: 0.0160 V Tuma swali linalofuata 📸