Refer to the circuit diagram given below. The heat generated across the 6 resistance in 100 second is 100 J. The value of is . (Nearest integer) [figure]
Answer
3477
Solution
[figure]
Take VY=0. The 2 V cell (positive plate on the left) makes the left wire +2 V. The 3 V cell (positive plate towards the 6 Ω) keeps the end of the 6 Ω resistor at +3 V. Let VX=V.
Junction rule at X (current in through 3 Ω = currents out through 4 Ω and 6 Ω):
2-V3= V-04+ V-36
× 12 ⇒ 8-4V=3V+2V-6 ⇒ 9V=14 ⇒ V= 149 V
Current in 6 Ω: i= 3-V6= 13/96= 1354 A (towards X)
Heat in 100 s: H=i2Rt= ( 1354 )2 6 100
= 1692916 600=34.77 J = 3477100 J
∴ =3477
Answer: 3477