Two batteries V ₁ and V ₂ are connected to three resistors as shown below. If V₁=2 V and V₂=0 ~V , the current I=3 ~mA . If V₁=0 ~V and V₂=4 V , the current I=4 ~mA . Now, if V ₁=10 ~V and V ₂=10 ~V , the current I will be-

Step-by-step solution

I = V _ eq R + R _ eq In each case R_ e q & R is same only V₁ & V₂ is changing V_ eq is changing V _ eq = 2 R ₂+0 R ₁ R ₁+ R ₂ [ ~V ₁=2, ~V ₂=0 ] V _ eq = 2 R ₂ R ₁+ R ₂ Case -2 ~V _ eq = 4 R ₁ R ₁+ R ₂ [ ~V ₁=0, ~V ₂=4 ] I ₁ I ₂ = 3 4 = 2 R ₂ 4 R ₁ R ₂ R ₁ = 3 2 Case - 3 ~V _ eq = 10 R ₁+10 R ₂ R ₁+ R ₂ 3 I ^ = 2 R ₂ 10 ( R ₁+ R ₂ ) 3 I ^ = 2 1.5 R ₁ 10 (2.5 R ₁ ) or I ^ =25 ~mA 3 I ^ = 2 R ₂ 10 ( R ₁+ R ₂ ) 3 I ^ = 2 1.5 R ₁ 10 (2.5 R ₁ ) or I ^ =25 ~mA