Math  /  Algebra

Question1. State the equation for current in a circuit where a capacitor is charging in terms of RR and CC. \qquad
2. State the equation for p.d. in a circuit where a capacitor is charging in terms of RR and CC. \qquad
3. State the equation for charge in a circuit where a capacitor is charging in terms of RR and CC. \qquad
4. State the equation for current in a circuit where a capacitor is discharging in terms of RR and CC. \qquad
15. State the equation for p.d. in a circuit where a capacitor is discharging in terms of RR and CC. \qquad
16. State the equation for charge in a circuit where a capacitor is discharging in terms of RR and CC. \qquad
17. Define the term time constant when referring to capacitors.

Studdy Solution

STEP 1

1. The circuit involves a resistor R R and a capacitor C C .
2. The equations will be expressed in terms of the time t t , resistance R R , capacitance C C , and initial values.
3. The time constant τ \tau is defined as τ=RC \tau = RC .

STEP 2

1. State the equation for current in a charging capacitor.
2. State the equation for potential difference (p.d.) in a charging capacitor.
3. State the equation for charge in a charging capacitor.
4. State the equation for current in a discharging capacitor.
5. State the equation for potential difference (p.d.) in a discharging capacitor.
6. State the equation for charge in a discharging capacitor.
7. Define the time constant for capacitors.

STEP 3

The equation for the current I(t) I(t) in a circuit where a capacitor is charging is given by:
I(t)=I0etRC I(t) = I_0 e^{-\frac{t}{RC}}
where I0 I_0 is the initial current at t=0 t = 0 .

STEP 4

The equation for the potential difference V(t) V(t) across a capacitor while it is charging is:
V(t)=V0(1etRC) V(t) = V_0 (1 - e^{-\frac{t}{RC}})
where V0 V_0 is the initial potential difference.

STEP 5

The equation for the charge Q(t) Q(t) on a capacitor while it is charging is:
Q(t)=Q0(1etRC) Q(t) = Q_0 (1 - e^{-\frac{t}{RC}})
where Q0 Q_0 is the maximum charge the capacitor can hold.

STEP 6

The equation for the current I(t) I(t) in a circuit where a capacitor is discharging is:
I(t)=I0etRC I(t) = I_0 e^{-\frac{t}{RC}}
where I0 I_0 is the initial current at t=0 t = 0 .

STEP 7

The equation for the potential difference V(t) V(t) across a capacitor while it is discharging is:
V(t)=V0etRC V(t) = V_0 e^{-\frac{t}{RC}}
where V0 V_0 is the initial potential difference.

STEP 8

The equation for the charge Q(t) Q(t) on a capacitor while it is discharging is:
Q(t)=Q0etRC Q(t) = Q_0 e^{-\frac{t}{RC}}
where Q0 Q_0 is the initial charge on the capacitor.

STEP 9

The time constant τ \tau for a capacitor in a circuit is defined as:
τ=RC \tau = RC
It represents the time required for the charge, current, or potential difference to decrease to approximately 36.8% of its initial value during discharging, or to increase to approximately 63.2% of its final value during charging.

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