A battery has an emf E=18.0V and an internal resistance r=1.00 ohm. Obtain the c

Question

A battery has an emf E=18.0V and an internal resistance r=1.00 ohm. Obtain the current I when the batter is connected to a resistor R=19.0 ohm. Also find the power P delivered to the wire by the battery and the value of the resistor for maximum value of P.

I=?

P=?

Rmax P=?

A battery has an emf E=18.0V and an internal resistance r=1.00 ohm. Obtain the current I when the batter is connected to a resistor R=19.0 ohm. Also find the power P delivered to the wire by the battery and the value of the resistor for maximum value of P. I=? P=? Rmax P=?

Explanation / Answer

emf - I r - I R = 0

18 - 1 I - 19 I = 0

20 I = 18

I = 0.9 A

b)
P = I^2 R = 0.9^2*19= 15.39 W
c)
I = emf/(r + R)

P = emf^2 R/(r + R)^2

dP/dR = emf^2/(r +R)^2 - 2 emf^2 R/(r+R)^3 = 0

emf^2 cancels and multiply both sides by (r +R)^3

r + R - 2 R = 0

Rmax = r = 1 ohm

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