In a Wheatstone's bridge all the four arms have equal resistance R. If the resistance of the galvanometer arm is also R, the equivalent resistance of the combination as seen by the battery is

In a Wheatstone Bridge, the four arms form a diamond shape with the battery connected across the top and bottom points and the galvanometer connected across the left and right points.

Step 1: Since all four arms of the Wheatstone Bridge have equal resistance (R), the bridge is balanced. This means that no current flows through the galvanometer.

Step 2: Because no current flows through the galvanometer, we can ignore its resistance when calculating the equivalent resistance of the combination.

Step 3: The equivalent resistance of the combination can be found by considering the top two resistors in series and the bottom two resistors in series. The resistance of two resistors in series is the sum of their resistances, so the resistance across the top is 2R and the resistance across the bottom is also 2R.

Step 4: These two sets of resistors (top and bottom) are then in parallel with each other. The equivalent resistance of two resistors in parallel is given by the formula 1/Re = 1/R1 + 1/R2.

Step 5: Substituting 2R for R1 and R2 in the formula gives 1/Re = 1/2R + 1/2R = 1/R.

Step 6: Solving for Re gives Re = R.

So, the equivalent resistance of the combination as seen by the battery is R.