Power of adding resistors in parallel
How does the power supplied by a battery change as you add more resistors to a circuit in parallel?
Since the voltage across each resistor is the same no matter how many resistors are added, the power dissipated by the resistors should stay the same no matter how many resistors you add, right?
Answer
The power dissipated through a resistor is P = V^2/R. You're right about the voltage being the same across all the resistors in parallel, but each resistor dissipates its own amount of power V^2/R. So the total power dissipated will increase.
Another way of looking at the situation is to treat all the resistors as a single resistor with an equivalent resistance. In parallel, the inverses of resistances are summed
1/R_effective = 1/R1 + 1/R2 + ...
If you plug in some values and solve for the effective resistance R_effective, you'll see that it has decreased. So the total power P = V^2/R_effective will thus increase.
Customer support service by UserEcho
The power dissipated through a resistor is P = V^2/R. You're right about the voltage being the same across all the resistors in parallel, but each resistor dissipates its own amount of power V^2/R. So the total power dissipated will increase.
Another way of looking at the situation is to treat all the resistors as a single resistor with an equivalent resistance. In parallel, the inverses of resistances are summed
1/R_effective = 1/R1 + 1/R2 + ...
If you plug in some values and solve for the effective resistance R_effective, you'll see that it has decreased. So the total power P = V^2/R_effective will thus increase.