What is the current in each resistor if a potential difference of 45 V is mainta

Question

What is the current in each resistor if a potential difference of 45 V is maintained between a Figure 28.9 The four and c? resistors shown in (a) can be reduced in steps to an Strategy Use Equations equivalent resistor shown 28.5, 28.7, and 27.8 in (c) Solution The circuit can be reduced in steps as shown in Figure 28.9. The 8.0 and r4.1 resistors are in eries, and so the equivalent resistance between a nd b is x-12.1 (see Eq. 28.5). The 6.0 a and 3.0 a sistors are in parallel, so from Equation 28.7 we find hat the equivalent resistance from b to c is 2.0 ?. Hence, what is the equivalent resistance from a to c? Using ??-IR and the results from part A, we have he following he current I in the 8.0 and 4.1 resistors is the ame because the resistors are in series. At the unction at b, the current splits. Part of it (I1) is in the 0 ° resistor, and part (12) is in the 30, resistor. Because the potential differences AVbc across these esistors are the same (they are in parallel), we see hatAVbc = IR = (6.0 ..)11 = (3.0 ..)12, or 12 = 2.011. Using this result and that I1 + I2 I, we find the lowing e could have guessed this result by noting that the urrent in the 3.0resistor has to be twice the current in the 6.0 resistor in view of their relative resistances nd that the same potential difference appears across ach of them a final check, note that ?Vh-(6.0-)11-(3.0 o I2 6.4 V and AVab (12.0 9I38.6 V thèrefore Exercise Hints: Getting Started I 8.4 Stuck Find the equivalent resistance of the following combination of resistors where eq

Explanation / Answer

Req= y = x+2 = 12.1+2 = 14.1

So, current I= 45/14.1= 3.2A

Also, I1+I2= 3.2

Or, I1+2I1= 3.2

So, I1= 3.2/3= 1.064A

I2= 2*1.064= 2.13A

Now,

R2 and R3 are in parallel so their equivalent is 3.9*8.1/3.9+8.1= 2.6325

This is in series with R1 and R4

so Req= 8+7.7+2.6345 = 18.3325 ohms

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