In the above circuit, if the current reading in the ammeter A is 2A, what would be the value of R1?

Ques:

In the above circuit, if the current reading in the ammeter A is 2A, what would be the value of R1?

Ans: 5 ohm, 10 ohm and R1 are in series
1/Rp = 1/5+1/10+1/R1
1/Rp = (2+1)/10 + 1/ R1
= 3/10 +1/ R1
1/Rp = (3 R1 +10)/10 R1
Rp= 10 R1 / (3 R1 +10)
Now, 6 ohm, 6 ohm and Rp are in series
Thus,
Req = 12 + 10 R1 / (3 R1 +10) —————— (1)

V = I Req
From the circuit
Req = 30/2 = 15 A —————(2)
Equating (1) and (2)
12 + 10 R1 / (3 R1 +10) = 15
10 R1 / (3 R1 +10) = 3
10 R1= (9 R1 + 30)
Thus, R1 = 30 ohm.