A) B) Four resistons are connected to a battery with a terminal voltage of 12 V,

Question

A)

B)

Four resistons are connected to a battery with a terminal voltage of 12 V, as shown in the figure below. (Assume R1 36.0 n and R2 76.0 n.) 50.0 n 12 V (a) How would you reduce the circuit to an equivalent single resistor connected to the battery? Use this procedure to find the equivalent resistance of the circuit (b) Find the current delivered by the battery to this equivalent resistance. (c) Determine the power delivered by the battery. (d) Determine the power delivered to the 50.0-n resistor.

Explanation / Answer

(1) ans

Here R1 and 50 ohms are series connection

resistance R=36+50=86 ohm

resistance R and R2 are parallel connection

resistance R'=86*76/86+76=6536/162=40.35 ohm

resistance R' and 20 ohm are series connection

the equivalent resistance Req=20+40.35=60.35 ohm

now we find the total current delivered by equivalent resistance

the total current I=V/Req=12/60.35=0.199 A

now we find the power delivered by battery

power P=VI=12*0.199=2.4 W

now we find the current on 50 ohms resistance

the current I4=86*0.199/86+76=0.11 A

power delivered in 50 ohms =>P4=i4^2*R=0.11^2*50=0.605 W

--------------------------------------------------------------------------------------------------------------------------------------------------------

(2) ans

applying kirchhoff's first law

i1+i2=i3...............................(1)

applying kirchhoff's second law for first loop

-18+10-29i1+5i2=0

29i1-5i2=8...........................(2)

applying kirchhoff's second law for second loop

5i2+24(i1+i2)=10

24i1+29i2=10...............(3)

now we solve eq2 &eq3 we get

eq2*29=>841i1-145i2=40

eq3*5 =>120i1+145i2=50

.......................................................

204i1=90

current i1=0.44 A

current i1 is substituting in eq 2 we get current i2

29(0.44)-5i2=8

12.8-5i2=8

5i2=4

current i2=0.8 A

current i3=0.8+0.44=1.24 A

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.