Resistor Current (A) Potential Difference (V) 4 ________ ________ R A (19) _____

Question

 

 

Resistor     Current (A)    Potential Difference (V)

4             ________       ________

RA  (19)     ________       ________

6             ________       ________

RB  (15)     ___________       ________

24           ________       ________

Consider the circuit shown in Figure P31.69, in which RA = 19 Resistor Current (A) Potential Difference (V) 4 OHM ________ ________ RA (19 OHM ) ________ ________ 6 OHM ________ ________ RB (15 OHM ) ___________ ________ 24 OHM ________ ________ . Tabulate the current through, and the potential difference across, each resistor. and RB = 15

Explanation / Answer

let the resistances in the circuit is r1 = 4 ohm, r2 =6 ohm, r3 = 24 ohm, RA=19 ohm, RB =15 ohm.

and the potential in the circuit V = 24v

RB and r3 are in parallel so the effective R4 = (RB*r3)/(RB+r3)

R4 = (15*24)/(15+24) = 360/39 = 9.23 ohm

this R4 is in series to r2 so effective R5 = 6+9.23 = 15.23 ohm

this R5 is parallel to RA so the effective R6 = (R5*RA)/(R5+RA)

R6 = (15.23*19)/(15.23+19) = 289.37/34.23 = 8.45 ohm

this R6 is in series to r1 so resultant in the circuit R = 4+8.45 = 12.45 ohm

the current in the circuit i = V/R = 24/12.45 = 1.93 amp

the current in 4 ohm resistor i4 = 1.93A and voltage v4 = i4*4 =7.72v

voltage across R6 effective resistance is V-v4 = 24-7.72 = 16.28v

current in 6ohm resistor i6 = 16.28 /15.23 = 1.07A and voltage v6 = i6*6 = 6.36v

current in 19 ohm resistor i19 = 16.28/19 = 0.86A and voltage v19 = 0.86*19 =16.28v

the voltage across R4 effective resistance Ve = 16.28 -v6 = 16.28-6.36 = 9.92v

current in 15 ohm resistor i15 = 9.92/15 =0.66A and voltage v15 = 9.92v

current in 24 ohm resistor i24 = 9.92/24 = 0.40A and voltage v24 =9.92v

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