When 4 equal resistors are connected in series with a battery they dissipate power of 10W. The power dissipated through any of them if connected across the same battery will be _____?

40 W

30 W

90 W

None of these

When four equal resistors are connected in series, the total resistance (R_total) is:

R_total = 4R

The power dissipated (P) is:

P = V² / R_total

Given P = 10 W, we can rewrite the equation as:

10 = V² / (4R)

Now, if one resistor is connected across the same battery, the power dissipated (P') will be:

P' = V² / R

Comparing the two equations, we can see that:

P' = 4P

= 4 × 10 W

= 40 W