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# D.C. circuits summary

## Summary of d.c. circuits

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.