# Problem: A resistor with resistance R and a capacitor with capacitance C are connected in series to an AC voltage source. The time-dependent voltage across the capacitor is given by VC(t) = VC0sinωt. If R = 3kΩ, C = 100 pF, VC0 = 100 mV, and ω = 105rad/s, what is VR?

###### FREE Expert Solution

Ohm's law:

$\overline{){\mathbf{V}}{\mathbf{=}}{\mathbf{i}}{\mathbf{R}}}$

Current through a capacitor:

$\overline{){\mathbf{i}}{\mathbf{=}}{\mathbf{C}}\frac{\mathbf{d}\mathbf{V}}{\mathbf{d}\mathbf{t}}}$

i = C(d/dt)VC0sinωt = CωVC0sinωt

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###### Problem Details

A resistor with resistance R and a capacitor with capacitance C are connected in series to an AC voltage source. The time-dependent voltage across the capacitor is given by VC(t) = VC0sinωt. If R = 3kΩ, C = 100 pF, VC0 = 100 mV, and ω = 105rad/s, what is VR?