### Related Formula V = IR$V = IR$ R_texteq = R_1 + R_2 + dots + R_n quad (textfor series)$R_{\text{eq}} = R_1 + R_2 + \dots + R_n \quad (\text{for series})$ ### Core Logic Observe the circuit diagram. The total equivalent resistance R_texteq$R_{\text{eq}}$ of the series network must be calculated by summing all the resistance values shown in the main branch. ### Step 1: Calculate Total Resistance and Current From the given network, assuming the total series resistance is 4000 \,Omega$4000 \,\Omega$ (comprising the 3.3mathrmkOmega$3.3\mathrm{k}\Omega$ resistor and seven 100\,Omega$100\,\Omega$ resistors). R_texteq = 4000 \,Omega$R_{\text{eq}} = 4000 \,\Omega$ The total voltage applied across the network is 4 mathrm~V$4 \mathrm{~V}$. i = fracVR_texteq = frac44000 = frac11000 mathrm~A$i = \frac{V}{R_{\text{eq}}} = \frac{4}{4000} = \frac{1}{1000} \mathrm{~A}$ ### Step 2: Calculate Output Voltage The output voltage V_0$V_0$ is tapped across five 100 \,Omega$100 \,\Omega$ resistors. R_textout = 5 times 100 \,Omega = 500 \,Omega$R_{\text{out}} = 5 \times 100 \,\Omega = 500 \,\Omega$ Thus, the output voltage is: V_0 = i cdot R_textout = left(frac11000right) times 500 = 0.5 mathrm~V$V_0 = i \cdot R_{\text{out}} = \left(\frac{1}{1000}\right) \times 500 = 0.5 \mathrm{~V}$ ### Pattern Recognition A potential divider simply scales the input voltage by the fraction of the resistance tapped over the total resistance: V_0 = V_in times (R_texttap / R_texttotal)$V_0 = V_{in} \times (R_{\text{tap}} / R_{\text{total}})$. Standard DC circuit division. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Current Electricity