Let's break down your question: **Given:** - R = 6 Ω (Resistor) - C = 7 μF (Capacitor) - L = 89 mH (Inductor) - You are asked to find the voltage "V" using KVL (Kirchhoff's Voltage Law). However, the circuit configuration is not explicitly given. But usually, with R, L, and C, it refers to a series RLC circuit. Assuming a **series RLC circuit** with an applied voltage \( V \): ### Step 1: Draw the Series RLC Circuit ``` ---[R]---[L]---[C]--- | | | V | ---------------------- ``` Where: - [R] = Resistor (6 Ω) - [L] = Inductor (89 mH) - [C] = Capacitor (7 μF) - A voltage source \( V \) is applied across the series combination. ### Step 2: Write KVL Equation By Kirchhoff's Voltage Law: \[ V = V_R + V_L + V_C \] Where: - \( V_R = iR \) (voltage across resistor) - \( V_L = L\frac{di}{dt} \) (voltage across inductor) - \( V_C = \frac{1}{C}\int i\,dt \) (voltage across capacitor) So, \[ V = iR + L\frac{di}{dt} + \frac{1}{C}\int i\,dt \] ### Step 3: Plug in Given Values Given: - \( R = 6\,\Omega \) - \( L = 89\,\text{mH} = 0.089\,\text{H} \) - \( C = 7\,\mu\text{F} = 7 \times 10^{-6}\,\text{F} \) So the equation becomes: \[ V = 6i + 0.089\frac{di}{dt} + \frac{1}{7\times 10^{-6}}\int i\,dt \] ### Step 4: Final KVL Equation The **KVL equation for this series RLC circuit** is: \[ \boxed{ V = 6i + 0.089\frac{di}{dt} + \frac{1}{7\times 10^{-6}}\int i\,dt } \] **Note:** - If you have the values for \( i \) or initial conditions, you can substitute them to find a numerical answer for \( V \) at a specific instant. - If an AC voltage \( V = V_0 \sin(\omega t) \) is applied, the analysis would involve phasors and impedance. --- **Summary:** 1. The KVL equation for the series RLC circuit is: \[ V = 6i + 0.089\frac{di}{dt} + \frac{1}{7\times 10^{-6}}\int i\,dt \] 2. This equation relates the applied voltage \( V \) to the current and its derivatives in the circuit. --- **If you have a specific value for current or a source voltage, let me know for a numerical answer!**