Find the total power consumed by the resistors if you know that the resistances of the resistors are 4

Find the total power consumed by the resistors if you know that the resistances of the resistors are 4 Ohms and 12 Ohms, and the EMF and the internal resistance of the source are 20 V and 1 Ohm, respectively.

R1 = 4 ohms.

R2 = 12 ohms.

r = 1 ohm.

EMF = 20 V.

N -?

The power N consumed by the resistors can be expressed by the formula: N = I * U or N = I2 * R, where I is the current strength, U is the voltage across the resistors, R is the resistance of the resistors.

Series connection of resistors.
R = R1 + R2, I = I1 = I2, U = U1 + U2.

I = EMF / (R + r) = EMF / (R1 + R2 + r).

I = 20 V / (4 Ohm + 12 Ohm + 1 Ohm) = 1.2 A.

U = R * I = (R1 + R2) * I.

U = (4 ohms + 12 ohms) * 1.2 A = 19.2 V.

N = 1.2 A * 19.2 V = 23 W.

Parallel connection of resistors.
R = R1 * R2 / (R1 + R2), I = I1 + I2, U = U1 = U2.

R = 4 ohms * 12 ohms / (4 ohms + 12 ohms) = 3 ohms.

I = EMF / (R + r).

I = 20 V / (3 Ohm + 1 Ohm) = 5 A.

N = (5 A) 2 * 3 Ohm = 75 W.

Answer: with a serial connection, the power is N = 23 W, with a parallel connection N = 75 W.




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