What is the value of R3? What is the current i1 through resistor R1? What is the

Question

What is the value of R3?

What is the current i1 through resistor R1?

What is the power P2 disipated in resistor R2?

Find the total resistance of the network.

Find the current drawn from the battery.

Find the total power used by the circuit

Three resistors are joined together across a 24 V battery (see the figure). The voltage drop across resistor R1 is 6.970 V, the current i2 through resistor R2 is 0.197 A, and the power dissipated in resistor R3 is 2.866 W. What is the value of R3? What is the current i1 through resistor R1? What is the power P2 disipated in resistor R2? Find the total resistance of the network. Find the current drawn from the battery. Find the total power used by the circuit

Explanation / Answer

We know that V1= 6.9 volts, I2=0.197 Amps, and P3=.2.86 Watts

We immediately know that V2=V3 and since VT = 24 volts,
V2=V3=VT-V1=24-6.9=17.1 volts.

Now P=IV and I=P/V so we have enough information to calculate I3=P3/V3=2.86 watts/17.1volts=0.167 amps

R3=V3/I3=17.1volts/0.16amps=102.3 ohms

Since we calculated V2 = 17.1 volts, the power through R2 is simply P2 = I2V2=0.197ampsx17.1volts=3.3 watts

R2=V2/I2=17.1volts/0.197amps=86.8 ohms

The sum of the currents through R2 and R2 is the current that goes through R1 so I1=I2+I3=0.197amps+0.16amps=0.36 amps.

R1=V1/I1=6.9volts/0.36 amps=19.1 ohms

Now we can calculate the power through R1. P1=I1V1=0.36ampsx6.9 volts=2.484 watts.

The total power PT=P1+P2+P3=2.88+3.2+2.48=8.64 watts

The total resistance is RT=VT/I=24volts/0.36amps=66.67 ohms

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