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
Here's how to solve the metre bridge problem: Step 1: Identify the knowns and the formula for a balanced metre bridge. In a balanced metre bridge, the ratio of resistances is equal to the ratio of the lengths of the wire segments. Given: Resistance R_1 = 30 \, Length L_1 = 40 \, cm (from A to the balance point) Total length of the wire is 100 \, cm. Therefore, the other length L_2 = 100 \, cm - L_1 = 100 \, cm - 40 \, cm = 60 \, cm. Unknown resistance R_2 = X. The formula for a balanced metre bridge is: (R_1)/(R_2) = (L_1)/(L_2) Step 2: Substitute the values into the formula. (30 \, )/(X) = 40 \, cm60 \, cm Step 3: Solve for X. (30)/(X) = (40)/(60) (30)/(X) = (2)/(3) 2X = 30 × 3 2X = 90 X = (90)/(2) X = 45 \, The magnitude of X is 45 . Here's the phasor diagram for the alternating currents: (i) Two alternating currents I_1 and I_2 are defined by the expression I_1 = I_0 ( t) and I_2 = I_0 ( t) respectively. Draw the phasor diagram to represent the currents I_1 and I_2. We can express I_1 in terms of cosine: I_1 = I_0 ( t) = I_0 ( t - ()/(2)). This means I_1 lags I_2 by ()/(2) (or 90^). The phasor diagram will show I_2 along the positive x-axis (representing ( t)) and I_1 along the negative y-axis (representing ( t - ()/(2))). Both phasors have the same amplitude I_0. % Axes [->] (-2,0) -- (2,0) node[right] Real Axis; [->] (0,-2) -- (0,2) node[above] Imaginary Axis; % Phasor I2 [->, thick, blue] (0,0) -- (1.5,0) node[above right] I_2 = I_0 ( t); % Phasor I1 [->, thick, red] (0,0) -- (0,-1.5) node[below right] I_1 = I_0 ( t); % Angle [dashed] (0,0) -- (1.5,0); [dashed] (0,0) -- (0,-1.5); [<->, gray] (0.5,0) arc (0:-90:0.5); [gray] at (0.7,-0.7) 90^; Last free one today — make it count tomorrow, or type /upgrade for unlimited.