Three resistors are joined together across a 24 Volts battery (see the figure).

Question

Three resistors are joined together across a 24 Volts battery (see the figure). The voltage drop across resistor R1 is 7.471 Volts, the current i2 through resistor R2 is 0.199 A, and the power dissipated in resistor R3 is 2.736 W.

What is the value of each resistor? R1? R2? R3?

What is the current through each resistor? i1? i3?

What is the power dissipated in each resistor? P1?

Find the total resistance of the network.

Find the current drawn from the battery.

Find the total power used by the circuit.

Explanation / Answer

V{R1} = 7.471 V

So, Voltage drop across R2 || R3 =V2 = V3 = 24 - 7.471 = 16.529 V

So, R2 = V2 / I2 = 83.06 ohm

R3 = V3^2 / P = 99.856 ohm

So, R3 || R2 = 45.34 ohm,

So current through (R3 || R2) =I1 = V / R = 0.364 Amp

So this current flows through R1...Hence R1 = V / I1 = 20.49 ohm

I3 = I1 - I2 = 0.165 Amp

P1 = I1 ^2 * R1 = 2.715 W

Total Resistance = R1 + (R2 ||R3) = 65.83 ohm

Total Current = V / R = 0.364 Amp

Total Power = V * I = 24 * 0.364 = 8.749 W

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