Question

The figure shows a circuit containing three switches, labeled S1, S2, and S3. Find the current at "a" for all possible combinations of switch settings. Put e = 90 V, R1 = 20 Ohm, and R2 = 10 Ohm. Assume that the battery has no resistance.
a. Current at "a" for S1 and S3 closed, S2 open (in A)

b. Current at "a" for S1 and S2 closed and S3 open (in A)

c. Current at "a" for SI and S2 and S3 open (in A)

Answer 1

a)

With S1 and S3 closed and S2 open circuit looks like above

equivalent resistance

From Right R₁ ,R₂ and R₂ are in series

R₁+R₂+R₂ =20+10+10=40 ohms

R1 and 40 ohms are in parallel

R2*40/(R1+40) =20*40/(20+40) =13.33 ohms

R1 and 13.33 are in series

R_eq =20+13.33 =33.33 ohms

Current from point a is

I_a =E/R_eq =90/33.33 =2.7 A

b)

With S1 and S2 closed ,S3 open circuit looks like above

equivalent resistance

From Right R1 and R2 are in series

R1+R2=20+10=30 ohms

R1 and 30 are in parallel

R1*30/(R1+30) =20*30/(20+30)=12 ohms

12 and R1 are in series

R_eq=12+R₁=12+20 =32 ohms

Current through point a

I_a=E/R_eq =90/32=2.8125 A

c)

Since all 3 swithces are open ,there is no path for current to flow ,so current through point a is zero i.e

I_a =0 A