The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ________ A.

### Related Formula For a balanced Wheatstone bridge network, if the potentials at opposite nodes are equal (V_A = V_B$V_A = V_B$), no current flows through the central branch. The resistance arms satisfy the balance ratio: fracR_1R_2 = fracR_3R_4$$\frac{R_1}{R_2} = \frac{R_3}{R_4}$$ Total current from the source is calculated using Ohm's law: I = fracV_textsourceR_textequivalent$$I = \frac{V_{\text{source}}}{R_{\text{equivalent}}}$$ ### Core Logic Given conditions : V_A = V_B implies textBalanced condition$$V_A = V_B \implies \text{Balanced condition}$$ From the circuit network diagram [cite: 817, 818, 826, 828]: * Left-top arm = 10 \ Omega$= 10 \ \Omega$ * Left-bottom arm = R$= R$ * Right-top arm = 20 \ Omega$= 20 \ \Omega$ * Right-bottom arm = 40 \ Omega$= 40 \ \Omega$ Apply the balance condition to solve for unknown resistor R$R$ : frac10R = frac2040 implies frac10R = frac12 implies R = 20 \ Omega quad text[cite: 837, 838]$$\frac{10}{R} = \frac{20}{40} \implies \frac{10}{R} = \frac{1}{2} \implies R = 20 \ \Omega \quad \text{[cite: 837, 838]}$$ Now restructure the equivalent network : Since the central 30 \ Omega$30 \ \Omega$ resistor branch carries zero current, it can be removed from the calculation [cite: 820, 834]. * Top \parallel branch: 10 \ Omega + 20 \ Omega = 30 \ Omega$10 \ \Omega + 20 \ \Omega = 30 \ \Omega$ * Bottom \parallel branch: 20 \ Omega + 40 \ Omega = 60 \ Omega$20 \ \Omega + 40 \ \Omega = 60 \ \Omega$ Calculate total equivalent resistance R_texteq$R_{\text{eq}}$: R_texteq = frac30 times 6030 + 60 = frac180090 = 20 \ Omega$$R_{\text{eq}} = \frac{30 \times 60}{30 + 60} = \frac{1800}{90} = 20 \ \Omega$$ Calculate total current I$I$ drawn from the 40textV$40\text{V}$ source: I = frac40 text V20 \ Omega = 2 text A$$I = \frac{40 \text{ V}}{20 \ \Omega} = 2 \text{ A}$$ ### Step 1: Circuit Solution The balanced bridge network layout with branch currents is shown below:

### Pattern Recognition When a question states that two nodes are at equal potential (V_A = V_B$V_A = V_B$), immediately identify it as a balanced Wheatstone bridge. This allows you to remove the central branch and simplify the circuit into basic series-\parallel resistor combinations. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Current Electricity