RMS value of current is given by

<tr> <td class=""> <p>0.707Im</p> </td> </tr>

{"methodBadge":"Direct Formula","steps":[{"title":"Understand the question","explanation":"The question asks for the RMS (Root Mean Square) value of current. RMS value of current is the square root of the mean of the squares of the values of the current.","highlight":"\\sqrt{\\frac{I_1^2 + I_2^2 + \\ldots + I_n^2}{n}}"},{"title":"Relate RMS current to peak current","explanation":"RMS current is related to the peak current by the formula $I_{rms} = \\frac{I_m}{\\sqrt{2}}$. This formula is derived by taking the square root of the mean of the squares of the values of the peak current.","highlight":"\\frac{I_m}{\\sqrt{2}}"},{"title":"Simplify the formula","explanation":"To simplify the formula, multiply the numerator and denominator by \\sqrt{2} to get $I_{rms} = \\frac{I_m}{\\sqrt{2}} \\times \\frac{\\sqrt{2}}{\\sqrt{2}} = \\frac{I_m \\sqrt{2}}{2}$","highlight":"\\frac{I_m \\sqrt{2}}{2}"},{"title":"Further simplify the formula","explanation":"This simplifies further to $\boxed{I_{rms} = 0.707I_m}$. Hence, the RMS value of current is $0.707$ times the peak value.","highlight":"0.707I_m"}],"answer":"A) 0.707Im. This is the correct answer because it correctly represents the relationship between RMS current and peak current.","coreConcepts":["AC Circuits","Peak and RMS Values","Phasor Analysis"],"crossTopicTip":"Understanding the relationship between peak and RMS values is crucial in topics such as power factor calculation and three-phase circuits."}