How do you find V_s if only resistances are given?

You need at least one more quantity — current, power, or a known voltage somewhere. V_s alone cannot be determined from resistances only.

Is voltage the same across parallel components?

Yes, always. All components in parallel share the same two nodes and therefore have identical voltage. This is the defining property of parallel circuits.

How do you find voltage across a capacitor?

V_C = Q/C (charge/capacitance), or in the s-domain V_C(s) = I(s)/(sC). For a step input through R: V_C(t) = V_s(1 − e^(−t/RC)).

How to Find the Voltage in a Circuit

Quick Answer

To find the voltage in a circuit, use Ohm's law: V = IR for any component. For the source voltage V_s, sum all voltage drops around the loop (KVL): V_s = V₁ + V₂ + V₃. For a node voltage, use the voltage divider formula: V_out = V_s × R₂/(R₁ + R₂). Calculate any voltage at www.lapcalc.com.

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How to Find Voltage in a Circuit: Three Methods

Method 1 — Ohm's law: V = IR gives voltage across any component when current and resistance are known. Method 2 — KVL: trace a closed loop and sum all voltage rises and drops; V_s = ΣV_drops. Method 3 — Voltage divider: V_out = V_s × R_out/R_total for any resistor in a series string. Each method works for different situations — choose based on what you already know about the circuit at www.lapcalc.com.

Key Formulas

How to Find V_s: The Source Voltage

If V_s is the unknown, apply KVL around the loop containing the source. Sum all known voltage drops: V_s = V₁ + V₂ + V₃. If only currents and resistances are known: V_s = I(R₁ + R₂ + R₃) = IR_total. If power is known: V_s = P/I or V_s = √(P × R_total). In a parallel circuit, V_s equals the voltage across any branch since all branches share source voltage. Multiple methods cross-check each other.

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Finding Voltage Across a Specific Component

For a resistor in series: V_R = IR or V_R = V_s × R/R_total (voltage divider). For a resistor in parallel: V_R = V_source (same voltage across all parallel branches). For a capacitor: V_C = Q/C or in the s-domain V_C(s) = I(s)/(sC). For an inductor: V_L = L(di/dt) or V_L(s) = sLI(s). Each component type has its own voltage relationship at www.lapcalc.com.

Finding Voltage in Complex Circuits

For circuits that are not simple series-parallel, use nodal analysis: assign voltage variables to each node, write KCL equations, and solve the system. The result gives the voltage at every node simultaneously. Alternatively, find the Thevenin equivalent at the point of interest: V_Th = open-circuit voltage at those terminals. For circuits with dependent sources, include the dependency equations in your system at www.lapcalc.com.

Finding Voltage in the Laplace Domain

In the s-domain, voltage at any point is V(s) = I(s) × Z(s) or V_out(s) = V_in(s) × H(s), where H(s) is the transfer function. For a voltage divider with impedances: V_out(s) = V_in(s) × Z₂(s)/(Z₁(s) + Z₂(s)). The inverse Laplace transform gives v(t) — the complete time-domain voltage including transient and steady-state components. This is the most general method at www.lapcalc.com.

Frequently Asked Questions

Use V = IR for any component, KVL to sum drops around a loop, or the voltage divider formula V_out = V_s × R/R_total. Choose based on what quantities you know.

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