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D.C. circuits summary

Direct current (d.c.) circuit: current flows in only one direction. Alternating current (a.c.) circuit: the direction of current changes at regular intervals.

Circuit Type Potential Difference $$(V)$$ Current $$(I)$$ Resistance $$(R)$$
Series $$$V_{T}=V_{1}+V_{2}$$$ $$$I_{T}=I_{1}=I_{2}$$$ $$$R_{T}=R_{1}+R_{2}$$$
Parallel $$$V_{T}=V_{1}=V_{2}$$$ $$$I_{T}=I_{1}+I_{2}$$$ $$$\frac{1}{R_{T}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$$$

Potential (or voltage) divider: output voltage $$V_{\text{o}}$$ is a fraction of the input voltage $$V_{\text{s}}$$.

$$$V_{1}=\frac{R_{1}}{R_{1}+R_{2}}\times V_{s}\quad\quad V_{2}=\frac{R_{2}}{R_{1}+R_{2}}\times V_{s}$$$

Devices that enable the variance of output voltage:

  • Moveable connector: pointer indicating the value of $$R$$.
  • Thermistors: $$T\text{ increases} \quad \Rightarrow \quad R\text{ decreases}$$
  • Light-dependent resistors (LDRs): $$\text{Light density increases}\quad \Rightarrow \quad R\text{ decreases}$$

Potentiometer: potential divider circuit that uses a resistance wire and a moveable connector to change the output voltage.

$$$\frac{V_{1}}{V_{s}}=\frac{\ell_{1}}{\ell}$$$

Cathode-ray oscilloscope (C.R.O.): instrument of measure that displays the waveforms of different types of electrical signals.

Vertical gain: voltage per division on the vertical axis ($$\text{V/cm}$$). Time-base: time per division on the horizontal axis ($$\text{ms/cm}$$).

$$V_{1/2}=$$ voltage across the output terminals; $$V_{s}=$$ voltage of the source; $$\ell_{1}=$$ distance between the moveable connector and the fixed terminal; $$\ell=$$ total length of the wire.