An uncharged capacitor and a resistor are connected in series to a source of emf. If E=9.00 V, C

An uncharged capacitor and a resistor are connected in...

Key Concepts

RC Circuit

An RC circuit consists of a resistor and a capacitor connected to a voltage source, typically in series or parallel arrangements. The resistor controls the rate at which charge flows into or out of the capacitor, while the capacitor stores electrical energy in an electric field. Analyzing RC circuits is fundamental in understanding transient responses, such as charging and discharging behaviors in electronics.

Time Constant (? = RC)

The time constant in an RC circuit is defined as the product of the resistance (R) and the capacitance (C). It represents the characteristic time over which the capacitor charges or discharges; specifically, during charging, after a time equal to one time constant, the capacitor will have reached approximately 63.2% of its maximum charge. This parameter is crucial for predicting the timing and behavior of transient responses in the circuit.

Maximum Charge on a Capacitor

The maximum charge that a capacitor can hold in a circuit is determined by the equation Q_max = CV, where C is the capacitance of the capacitor and V is the applied voltage. This value represents the equilibrium state when the capacitor is fully charged and no further current flows in the circuit, serving as a benchmark for analyzing transient charging processes.

Exponential Charging of a Capacitor

When connected to a voltage source through a resistor, a capacitor charges following an exponential growth pattern described by the equation Q(t) = Q_max (1 - exp(-t/RC)). This equation captures the gradual increase in charge over time as the capacitor approaches its maximum charge, with the time constant (RC) governing the rate of this process.

Transcript

00:01 As per the given data, there is uncharged capacitor which is connected in series with the register and the battery.

00:08 The respective values are written.

00:11 Now, we need to find the time constant of the circuit.

00:16 So basically, we'll write here, the time constant of the circuit is denoted as tau.

00:36 This is a symbol.

00:38 So therefore, tau is the product of register.

00:43 And the capacitor.

00:45 So let's write the values which are given.

00:48 R is equal to 100 oms and the capacitor value is given as 20 microferral.

00:56 So that is 20 into 10 to minus 6 ferrets.

01:01 Therefore for the calculation will be tau is equal to 2000 into 10 to minus 6 which is equal to 2 into 10x2 minus 6 which is equal to 2 into 10 minus 3.

01:19 Seconds because tau that is time constant is measured in seconds so therefore we'll write the time constant of the circuit is 2 milliseconds and we'll put this in bracket that is the answer to the step a now let's see the step b we need to find the maximum charge on the capacitor so we'll just write down that is we find maximum charge on capacitor that is what we need to find out now we'll make the use of this equation that is q is equal to c multiplied by emf now here q stands for the charge in columns we'll write down charge in coulomes here c stands for the capacitance which is majored infrareds and e stands for emf that is measured in volts so we need to understand that so when we may even write a note if you want when emf of the battery will write down when emf of battery is equal to the potential difference the charge on the capacitor will be maximum so therefore in order to calculate q max that is maximum charge in the capacitor will make use of this equation which we already have written is equal to charge on the capacitor is no we are talking about the capacitance so it is 20 micro so 20 into 10 10 x multiplied by battery voltage that is 9 volts so finally we get the value as 180 into 10 .0 .10 to minus 6 columns.

04:16 So write down and that will be our answer.

04:20 That is maximum charge on capacitor is 180 microcoloms.

04:34 And this will be our final answer for the step b.

04:43 Let's talk about next step.

04:47 Step c.

04:50 We need to find charge on the capacitor after one time constant...

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